← Find the pair first, then let the ratio cut it · Read and Scale a Data Graph

Find the pair first, then let the ratio cut it · 12 practice problems

6.RP.A.3

Generated variants — 12

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

Variant 1 easy answer: Family clinics 8%, oriental clinics 40%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 1:51 : 5, what percent of the total is each?

Share of medical facilities by type Pharmacies 20% Family Oriental Dental 16% Other 16%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 20 percent, dental clinics 16 percent and other 16 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 5. We want each of their percentages.

Givens
  • Pharmacies are 20 percent, dental clinics 16 percent, other 16 percent.
  • Family clinics to oriental clinics is 1 to 5.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−20−16−16=48100 - 20 - 16 - 16 = 48
The two clinics share 48 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
1 to 5 means 6 equal parts, 1 of them family and 5 oriental.
48÷6=848 \div 6 = 8
Each part is 8 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 1 parts and oriental clinics 5.
8×1=8,8×5=408 \times 1 = 8,\quad 8 \times 5 = 40
8 percent and 40 percent.
Answer: Family clinics 8%, oriental clinics 40%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 8 to 40 simplifies back to 1 to 5.

Another way: Splitting the 48 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 2 easy answer: Family clinics 7%, oriental clinics 49%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 1:71 : 7, what percent of the total is each?

Share of medical facilities by type Pharmacies 20% Family Oriental Dental 9% Other 15%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 20 percent, dental clinics 9 percent and other 15 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 7. We want each of their percentages.

Givens
  • Pharmacies are 20 percent, dental clinics 9 percent, other 15 percent.
  • Family clinics to oriental clinics is 1 to 7.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−20−9−15=56100 - 20 - 9 - 15 = 56
The two clinics share 56 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
1 to 7 means 8 equal parts, 1 of them family and 7 oriental.
56÷8=756 \div 8 = 7
Each part is 7 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 1 parts and oriental clinics 7.
7×1=7,7×7=497 \times 1 = 7,\quad 7 \times 7 = 49
7 percent and 49 percent.
Answer: Family clinics 7%, oriental clinics 49%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 7 to 49 simplifies back to 1 to 7.

Another way: Splitting the 56 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 3 easy answer: Family clinics 21%, oriental clinics 42%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 1:21 : 2, what percent of the total is each?

Share of medical facilities by type Pharmacies 23% Family Oriental Dental 9% Other 5%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 23 percent, dental clinics 9 percent and other 5 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 2. We want each of their percentages.

Givens
  • Pharmacies are 23 percent, dental clinics 9 percent, other 5 percent.
  • Family clinics to oriental clinics is 1 to 2.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−23−9−5=63100 - 23 - 9 - 5 = 63
The two clinics share 63 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
1 to 2 means 3 equal parts, 1 of them family and 2 oriental.
63÷3=2163 \div 3 = 21
Each part is 21 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 1 parts and oriental clinics 2.
21×1=21,21×2=4221 \times 1 = 21,\quad 21 \times 2 = 42
21 percent and 42 percent.
Answer: Family clinics 21%, oriental clinics 42%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 21 to 42 simplifies back to 1 to 2.

Another way: Splitting the 63 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 4 easy answer: Family clinics 27%, oriental clinics 18%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 3:23 : 2, what percent of the total is each?

Share of medical facilities by type Pharmacies 24% Family Oriental Dental 12% Other 19%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 24 percent, dental clinics 12 percent and other 19 percent. Family and oriental clinics are unlabelled and stand in the ratio 3 to 2. We want each of their percentages.

Givens
  • Pharmacies are 24 percent, dental clinics 12 percent, other 19 percent.
  • Family clinics to oriental clinics is 3 to 2.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−24−12−19=45100 - 24 - 12 - 19 = 45
The two clinics share 45 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
3 to 2 means 5 equal parts, 3 of them family and 2 oriental.
45÷5=945 \div 5 = 9
Each part is 9 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 3 parts and oriental clinics 2.
9×3=27,9×2=189 \times 3 = 27,\quad 9 \times 2 = 18
27 percent and 18 percent.
Answer: Family clinics 27%, oriental clinics 18%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 27 to 18 simplifies back to 3 to 2.

Another way: Splitting the 45 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 5 medium answer: Family clinics 28%, oriental clinics 16%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 7:47 : 4, what percent of the total is each?

Share of medical facilities by type Pharmacies 30% Family Oriental Dental 21% Other 5%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 30 percent, dental clinics 21 percent and other 5 percent. Family and oriental clinics are unlabelled and stand in the ratio 7 to 4. We want each of their percentages.

Givens
  • Pharmacies are 30 percent, dental clinics 21 percent, other 5 percent.
  • Family clinics to oriental clinics is 7 to 4.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−30−21−5=44100 - 30 - 21 - 5 = 44
The two clinics share 44 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
7 to 4 means 11 equal parts, 7 of them family and 4 oriental.
44÷11=444 \div 11 = 4
Each part is 4 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 7 parts and oriental clinics 4.
4×7=28,4×4=164 \times 7 = 28,\quad 4 \times 4 = 16
28 percent and 16 percent.
Answer: Family clinics 28%, oriental clinics 16%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 28 to 16 simplifies back to 7 to 4.

Another way: Splitting the 44 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 6 medium answer: Family clinics 20%, oriental clinics 28%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 5:75 : 7, what percent of the total is each?

Share of medical facilities by type Pharmacies 30% Family Oriental Dental 11% Other 11%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 30 percent, dental clinics 11 percent and other 11 percent. Family and oriental clinics are unlabelled and stand in the ratio 5 to 7. We want each of their percentages.

Givens
  • Pharmacies are 30 percent, dental clinics 11 percent, other 11 percent.
  • Family clinics to oriental clinics is 5 to 7.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−30−11−11=48100 - 30 - 11 - 11 = 48
The two clinics share 48 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
5 to 7 means 12 equal parts, 5 of them family and 7 oriental.
48÷12=448 \div 12 = 4
Each part is 4 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 5 parts and oriental clinics 7.
4×5=20,4×7=284 \times 5 = 20,\quad 4 \times 7 = 28
20 percent and 28 percent.
Answer: Family clinics 20%, oriental clinics 28%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 20 to 28 simplifies back to 5 to 7.

Another way: Splitting the 48 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 7 medium answer: Family clinics 33%, oriental clinics 11%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 3:13 : 1, what percent of the total is each?

Share of medical facilities by type Pharmacies 36% Family Oriental Dental 11% Other 9%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 36 percent, dental clinics 11 percent and other 9 percent. Family and oriental clinics are unlabelled and stand in the ratio 3 to 1. We want each of their percentages.

Givens
  • Pharmacies are 36 percent, dental clinics 11 percent, other 9 percent.
  • Family clinics to oriental clinics is 3 to 1.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−36−11−9=44100 - 36 - 11 - 9 = 44
The two clinics share 44 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
3 to 1 means 4 equal parts, 3 of them family and 1 oriental.
44÷4=1144 \div 4 = 11
Each part is 11 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 3 parts and oriental clinics 1.
11×3=33,11×1=1111 \times 3 = 33,\quad 11 \times 1 = 11
33 percent and 11 percent.
Answer: Family clinics 33%, oriental clinics 11%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 33 to 11 simplifies back to 3 to 1.

Another way: Splitting the 44 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 8 medium answer: Family clinics 33%, oriental clinics 11%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 3:13 : 1, what percent of the total is each?

Share of medical facilities by type Pharmacies 40% Family Oriental Dental 10% Other 6%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 40 percent, dental clinics 10 percent and other 6 percent. Family and oriental clinics are unlabelled and stand in the ratio 3 to 1. We want each of their percentages.

Givens
  • Pharmacies are 40 percent, dental clinics 10 percent, other 6 percent.
  • Family clinics to oriental clinics is 3 to 1.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−40−10−6=44100 - 40 - 10 - 6 = 44
The two clinics share 44 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
3 to 1 means 4 equal parts, 3 of them family and 1 oriental.
44÷4=1144 \div 4 = 11
Each part is 11 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 3 parts and oriental clinics 1.
11×3=33,11×1=1111 \times 3 = 33,\quad 11 \times 1 = 11
33 percent and 11 percent.
Answer: Family clinics 33%, oriental clinics 11%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 33 to 11 simplifies back to 3 to 1.

Another way: Splitting the 44 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 9 hard answer: Family clinics 7%, oriental clinics 14%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 1:21 : 2, what percent of the total is each?

Share of medical facilities by type Pharmacies 41% Family Oriental Dental 21% Other 17%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 41 percent, dental clinics 21 percent and other 17 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 2. We want each of their percentages.

Givens
  • Pharmacies are 41 percent, dental clinics 21 percent, other 17 percent.
  • Family clinics to oriental clinics is 1 to 2.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−41−21−17=21100 - 41 - 21 - 17 = 21
The two clinics share 21 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
1 to 2 means 3 equal parts, 1 of them family and 2 oriental.
21÷3=721 \div 3 = 7
Each part is 7 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 1 parts and oriental clinics 2.
7×1=7,7×2=147 \times 1 = 7,\quad 7 \times 2 = 14
7 percent and 14 percent.
Answer: Family clinics 7%, oriental clinics 14%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 7 to 14 simplifies back to 1 to 2.

Another way: Splitting the 21 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 10 hard answer: Family clinics 25%, oriental clinics 15%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 5:35 : 3, what percent of the total is each?

Share of medical facilities by type Pharmacies 42% Family Oriental Dental 13% Other 5%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 42 percent, dental clinics 13 percent and other 5 percent. Family and oriental clinics are unlabelled and stand in the ratio 5 to 3. We want each of their percentages.

Givens
  • Pharmacies are 42 percent, dental clinics 13 percent, other 5 percent.
  • Family clinics to oriental clinics is 5 to 3.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−42−13−5=40100 - 42 - 13 - 5 = 40
The two clinics share 40 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
5 to 3 means 8 equal parts, 5 of them family and 3 oriental.
40÷8=540 \div 8 = 5
Each part is 5 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 5 parts and oriental clinics 3.
5×5=25,5×3=155 \times 5 = 25,\quad 5 \times 3 = 15
25 percent and 15 percent.
Answer: Family clinics 25%, oriental clinics 15%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 25 to 15 simplifies back to 5 to 3.

Another way: Splitting the 40 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 11 hard answer: Family clinics 6%, oriental clinics 36%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 1:61 : 6, what percent of the total is each?

Share of medical facilities by type Pharmacies 45% Family Oriental Dental 10% Other 3%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 45 percent, dental clinics 10 percent and other 3 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 6. We want each of their percentages.

Givens
  • Pharmacies are 45 percent, dental clinics 10 percent, other 3 percent.
  • Family clinics to oriental clinics is 1 to 6.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−45−10−3=42100 - 45 - 10 - 3 = 42
The two clinics share 42 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
1 to 6 means 7 equal parts, 1 of them family and 6 oriental.
42÷7=642 \div 7 = 6
Each part is 6 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 1 parts and oriental clinics 6.
6×1=6,6×6=366 \times 1 = 6,\quad 6 \times 6 = 36
6 percent and 36 percent.
Answer: Family clinics 6%, oriental clinics 36%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 6 to 36 simplifies back to 1 to 6.

Another way: Splitting the 42 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.
Variant 12 hard answer: Family clinics 15%, oriental clinics 3%

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is 5:15 : 1, what percent of the total is each?

Share of medical facilities by type Pharmacies 48% Family Oriental Dental 15% Other 19%
Show solution
1 · Understandwhat's really being asked

A bar graph gives pharmacies 48 percent, dental clinics 15 percent and other 19 percent. Family and oriental clinics are unlabelled and stand in the ratio 5 to 1. We want each of their percentages.

Givens
  • Pharmacies are 48 percent, dental clinics 15 percent, other 19 percent.
  • Family clinics to oriental clinics is 5 to 1.
Unknowns
  • The percentage for family clinics and for oriental clinics.
Constraints
  • The five sections together are 100 percent.
2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3
The five sections make 100 percent, so subtract the three that are labelled.
100−48−15−19=18100 - 48 - 15 - 19 = 18
The two clinics share 18 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3
5 to 1 means 6 equal parts, 5 of them family and 1 oriental.
18÷6=318 \div 6 = 3
Each part is 3 percent.

3Give each its share

#8 Analyze the Units 6.RP.A.3
Family clinics take 5 parts and oriental clinics 1.
3×5=15,3×1=33 \times 5 = 15,\quad 3 \times 1 = 3
15 percent and 3 percent.
Answer: Family clinics 15%, oriental clinics 3%
4 · Reviewdoes it hold up?

All five add to 100 percent, and 15 to 3 simplifies back to 5 to 1.

Another way: Splitting the 18 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.
💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.