← A percentage always needs the whole it belongs to · Read and Scale a Data Graph

A percentage always needs the whole it belongs to · 12 practice problems

7.RP.A.36.SP.B.5

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 9 g

A fish weighs $100\ \text{g}$ , and $40\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 100 g fish is 40 percent inedible. The edible part is 66 percent water, 10 percent fat and 9 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 100 g.
40 percent of it cannot be eaten.
Of the edible part: water 66 percent, fat 10 percent, other 9 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 40 percent cannot be eaten, 60 percent can.

100 \times 0.6 = 60

60 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 66 - 10 - 9 = 15

Protein is 15 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

60 \times 0.15 = 9

9 g of protein.

Answer: 9 g

4 · Reviewdoes it hold up?

9 g out of the 60 g edible part is 15 percent, and out of the whole 100 g fish it is only 9 percent -- less, as it must be.

Another way: Taking 15 percent of the whole 100 g fish gives 15 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 2 easy answer: 15 g

A fish weighs $100\ \text{g}$ , and $40\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 100 g fish is 40 percent inedible. The edible part is 70 percent water, 3 percent fat and 2 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 100 g.
40 percent of it cannot be eaten.
Of the edible part: water 70 percent, fat 3 percent, other 2 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 40 percent cannot be eaten, 60 percent can.

100 \times 0.6 = 60

60 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 70 - 3 - 2 = 25

Protein is 25 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

60 \times 0.25 = 15

15 g of protein.

Answer: 15 g

4 · Reviewdoes it hold up?

15 g out of the 60 g edible part is 25 percent, and out of the whole 100 g fish it is only 15 percent -- less, as it must be.

Another way: Taking 25 percent of the whole 100 g fish gives 25 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 3 easy answer: 18 g

A fish weighs $120\ \text{g}$ , and $25\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 120 g fish is 25 percent inedible. The edible part is 72 percent water, 5 percent fat and 3 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 120 g.
25 percent of it cannot be eaten.
Of the edible part: water 72 percent, fat 5 percent, other 3 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 25 percent cannot be eaten, 75 percent can.

120 \times 0.75 = 90

90 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 72 - 5 - 3 = 20

Protein is 20 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

90 \times 0.2 = 18

18 g of protein.

Answer: 18 g

4 · Reviewdoes it hold up?

18 g out of the 90 g edible part is 20 percent, and out of the whole 120 g fish it is only 15 percent -- less, as it must be.

Another way: Taking 20 percent of the whole 120 g fish gives 24 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 4 easy answer: 22 g

A fish weighs $160\ \text{g}$ , and $45\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 160 g fish is 45 percent inedible. The edible part is 70 percent water, 3 percent fat and 2 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 160 g.
45 percent of it cannot be eaten.
Of the edible part: water 70 percent, fat 3 percent, other 2 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 45 percent cannot be eaten, 55 percent can.

160 \times 0.55 = 88

88 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 70 - 3 - 2 = 25

Protein is 25 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

88 \times 0.25 = 22

22 g of protein.

Answer: 22 g

4 · Reviewdoes it hold up?

22 g out of the 88 g edible part is 25 percent, and out of the whole 160 g fish it is only 13.75 percent -- less, as it must be.

Another way: Taking 25 percent of the whole 160 g fish gives 40 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 5 medium answer: 19 g

A fish weighs $200\ \text{g}$ , and $50\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 200 g fish is 50 percent inedible. The edible part is 72 percent water, 3 percent fat and 6 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 200 g.
50 percent of it cannot be eaten.
Of the edible part: water 72 percent, fat 3 percent, other 6 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 50 percent cannot be eaten, 50 percent can.

200 \times 0.5 = 100

100 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 72 - 3 - 6 = 19

Protein is 19 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

100 \times 0.19 = 19

19 g of protein.

Answer: 19 g

4 · Reviewdoes it hold up?

19 g out of the 100 g edible part is 19 percent, and out of the whole 200 g fish it is only 9.5 percent -- less, as it must be.

Another way: Taking 19 percent of the whole 200 g fish gives 38 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 6 medium answer: 27 g

A fish weighs $300\ \text{g}$ , and $25\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 300 g fish is 25 percent inedible. The edible part is 76 percent water, 9 percent fat and 3 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 300 g.
25 percent of it cannot be eaten.
Of the edible part: water 76 percent, fat 9 percent, other 3 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 25 percent cannot be eaten, 75 percent can.

300 \times 0.75 = 225

225 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 76 - 9 - 3 = 12

Protein is 12 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

225 \times 0.12 = 27

27 g of protein.

Answer: 27 g

4 · Reviewdoes it hold up?

27 g out of the 225 g edible part is 12 percent, and out of the whole 300 g fish it is only 9 percent -- less, as it must be.

Another way: Taking 12 percent of the whole 300 g fish gives 36 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 7 medium answer: 24 g

A fish weighs $400\ \text{g}$ , and $40\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 400 g fish is 40 percent inedible. The edible part is 74 percent water, 7 percent fat and 9 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 400 g.
40 percent of it cannot be eaten.
Of the edible part: water 74 percent, fat 7 percent, other 9 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 40 percent cannot be eaten, 60 percent can.

400 \times 0.6 = 240

240 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 74 - 7 - 9 = 10

Protein is 10 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

240 \times 0.1 = 24

24 g of protein.

Answer: 24 g

4 · Reviewdoes it hold up?

24 g out of the 240 g edible part is 10 percent, and out of the whole 400 g fish it is only 6 percent -- less, as it must be.

Another way: Taking 10 percent of the whole 400 g fish gives 40 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 8 medium answer: 66 g

A fish weighs $440\ \text{g}$ , and $25\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 440 g fish is 25 percent inedible. The edible part is 68 percent water, 2 percent fat and 10 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 440 g.
25 percent of it cannot be eaten.
Of the edible part: water 68 percent, fat 2 percent, other 10 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 25 percent cannot be eaten, 75 percent can.

440 \times 0.75 = 330

330 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 68 - 2 - 10 = 20

Protein is 20 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

330 \times 0.2 = 66

66 g of protein.

Answer: 66 g

4 · Reviewdoes it hold up?

66 g out of the 330 g edible part is 20 percent, and out of the whole 440 g fish it is only 15 percent -- less, as it must be.

Another way: Taking 20 percent of the whole 440 g fish gives 88 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 9 hard answer: 69 g

A fish weighs $460\ \text{g}$ , and $25\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 460 g fish is 25 percent inedible. The edible part is 69 percent water, 4 percent fat and 7 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 460 g.
25 percent of it cannot be eaten.
Of the edible part: water 69 percent, fat 4 percent, other 7 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 25 percent cannot be eaten, 75 percent can.

460 \times 0.75 = 345

345 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 69 - 4 - 7 = 20

Protein is 20 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

345 \times 0.2 = 69

69 g of protein.

Answer: 69 g

4 · Reviewdoes it hold up?

69 g out of the 345 g edible part is 20 percent, and out of the whole 460 g fish it is only 15 percent -- less, as it must be.

Another way: Taking 20 percent of the whole 460 g fish gives 92 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 10 hard answer: 35 g

A fish weighs $500\ \text{g}$ , and $50\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 500 g fish is 50 percent inedible. The edible part is 69 percent water, 8 percent fat and 9 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 500 g.
50 percent of it cannot be eaten.
Of the edible part: water 69 percent, fat 8 percent, other 9 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 50 percent cannot be eaten, 50 percent can.

500 \times 0.5 = 250

250 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 69 - 8 - 9 = 14

Protein is 14 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

250 \times 0.14 = 35

35 g of protein.

Answer: 35 g

4 · Reviewdoes it hold up?

35 g out of the 250 g edible part is 14 percent, and out of the whole 500 g fish it is only 7 percent -- less, as it must be.

Another way: Taking 14 percent of the whole 500 g fish gives 70 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 11 hard answer: 15 g

A fish weighs $500\ \text{g}$ , and $50\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 500 g fish is 50 percent inedible. The edible part is 77 percent water, 8 percent fat and 9 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 500 g.
50 percent of it cannot be eaten.
Of the edible part: water 77 percent, fat 8 percent, other 9 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 50 percent cannot be eaten, 50 percent can.

500 \times 0.5 = 250

250 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 77 - 8 - 9 = 6

Protein is 6 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

250 \times 0.06 = 15

15 g of protein.

Answer: 15 g

4 · Reviewdoes it hold up?

15 g out of the 250 g edible part is 6 percent, and out of the whole 500 g fish it is only 3 percent -- less, as it must be.

Another way: Taking 6 percent of the whole 500 g fish gives 30 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.

Variant 12 hard answer: 48 g

A fish weighs $500\ \text{g}$ , and $20\%$ of it cannot be eaten. The circle graph at the right shows what the edible part is made of. How many grams of protein does eating one fish provide?

Show solution

1 · Understandwhat's really being asked

A 500 g fish is 20 percent inedible. The edible part is 74 percent water, 9 percent fat and 5 percent other, with protein unlabelled. We want the protein in grams.

Givens

The fish weighs 500 g.
20 percent of it cannot be eaten.
Of the edible part: water 74 percent, fat 9 percent, other 5 percent.

Unknowns

The grams of protein in one fish.

Constraints

The graph's percentages are shares of the edible part, not of the whole fish.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#16 Count the Complement

Two percentages, two different wholes. Shrink the fish to its edible part first, and only then let the graph's percentages act -- they were never percentages of the fish.

3 · Execute3 carry out the plan

1Find the edible part

#7 Identify Subproblems 7.RP.A.3

If 20 percent cannot be eaten, 80 percent can.

500 \times 0.8 = 400

400 g is worth eating.

2Find the protein's share of that

#16 Count the Complement 6.SP.B.5

The four nutrients make the whole edible part, so protein is what the other three leave.

100 - 74 - 9 - 5 = 12

Protein is 12 percent of the edible part.

3Take that share of the edible part

#8 Analyze the Units 7.RP.A.3

The percentage belongs to the edible weight, not the whole fish.

400 \times 0.12 = 48

48 g of protein.

Answer: 48 g

4 · Reviewdoes it hold up?

48 g out of the 400 g edible part is 12 percent, and out of the whole 500 g fish it is only 9.6 percent -- less, as it must be.

Another way: Taking 12 percent of the whole 500 g fish gives 60 g, which is too big: that treats the graph as if it described the fish rather than its edible part.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Applying two percentages in turn, each to its own whole.
6.SP.B.5 Summarize numerical data sets in relation to context — Reading the unlabelled slice as what the others leave.

💡Takeaway. Always ask what a percentage is a percentage OF. Two percentages in one problem often mean two different wholes.