Practice · Percentages of different groups compare only through counts · Sensim Math

Variant 1 easy

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $150$ boys in all, and $6$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

150 boys are split by hobby, 20 percent of them reading. The girls' graph gives reading 30 percent, and 6 more girls than boys read. We want the number of girls.

Givens

There are 150 boys.
Reading is 20 percent of the boys and 30 percent of the girls.
6 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

20 percent and 30 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

20 percent of the 150 boys.

150 \times 0.2 = 30

30 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

6 more than the boys.

30 + 6 = 36

36 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 36 girls are 30 percent of all the girls.

\text{girls} \times 0.3 = 36

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

36 \div 0.3 = 120

There are 120 girls.

Answer: 120 girls

4 · Reviewdoes it hold up?

30 percent of 120 girls is 36 readers, which is 6 more than the boys' 30 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read more, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 2 easy

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $150$ boys in all, and $20$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

150 boys are split by hobby, 30 percent of them reading. The girls' graph gives reading 25 percent, and 20 more girls than boys read. We want the number of girls.

Givens

There are 150 boys.
Reading is 30 percent of the boys and 25 percent of the girls.
20 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

30 percent and 25 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

30 percent of the 150 boys.

150 \times 0.3 = 45

45 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

20 more than the boys.

45 + 20 = 65

65 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 65 girls are 25 percent of all the girls.

\text{girls} \times 0.25 = 65

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

65 \div 0.25 = 260

There are 260 girls.

Answer: 260 girls

4 · Reviewdoes it hold up?

25 percent of 260 girls is 65 readers, which is 20 more than the boys' 45 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read less, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 3 easy

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $160$ boys in all, and $20$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

160 boys are split by hobby, 20 percent of them reading. The girls' graph gives reading 25 percent, and 20 more girls than boys read. We want the number of girls.

Givens

There are 160 boys.
Reading is 20 percent of the boys and 25 percent of the girls.
20 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

20 percent and 25 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

20 percent of the 160 boys.

160 \times 0.2 = 32

32 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

20 more than the boys.

32 + 20 = 52

52 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 52 girls are 25 percent of all the girls.

\text{girls} \times 0.25 = 52

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

52 \div 0.25 = 208

There are 208 girls.

Answer: 208 girls

4 · Reviewdoes it hold up?

25 percent of 208 girls is 52 readers, which is 20 more than the boys' 32 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read more, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 4 easy

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $200$ boys in all, and $5$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

200 boys are split by hobby, 28 percent of them reading. The girls' graph gives reading 20 percent, and 5 more girls than boys read. We want the number of girls.

Givens

There are 200 boys.
Reading is 28 percent of the boys and 20 percent of the girls.
5 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

28 percent and 20 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

28 percent of the 200 boys.

200 \times 0.28 = 56

56 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

5 more than the boys.

56 + 5 = 61

61 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 61 girls are 20 percent of all the girls.

\text{girls} \times 0.2 = 61

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

61 \div 0.2 = 305

There are 305 girls.

Answer: 305 girls

4 · Reviewdoes it hold up?

20 percent of 305 girls is 61 readers, which is 5 more than the boys' 56 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read less, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 5 medium

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $200$ boys in all, and $6$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

200 boys are split by hobby, 24 percent of them reading. The girls' graph gives reading 15 percent, and 6 more girls than boys read. We want the number of girls.

Givens

There are 200 boys.
Reading is 24 percent of the boys and 15 percent of the girls.
6 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

24 percent and 15 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

24 percent of the 200 boys.

200 \times 0.24 = 48

48 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

6 more than the boys.

48 + 6 = 54

54 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 54 girls are 15 percent of all the girls.

\text{girls} \times 0.15 = 54

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

54 \div 0.15 = 360

There are 360 girls.

Answer: 360 girls

4 · Reviewdoes it hold up?

15 percent of 360 girls is 54 readers, which is 6 more than the boys' 48 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read less, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 6 medium

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $200$ boys in all, and $6$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

200 boys are split by hobby, 28 percent of them reading. The girls' graph gives reading 25 percent, and 6 more girls than boys read. We want the number of girls.

Givens

There are 200 boys.
Reading is 28 percent of the boys and 25 percent of the girls.
6 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

28 percent and 25 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

28 percent of the 200 boys.

200 \times 0.28 = 56

56 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

6 more than the boys.

56 + 6 = 62

62 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 62 girls are 25 percent of all the girls.

\text{girls} \times 0.25 = 62

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

62 \div 0.25 = 248

There are 248 girls.

Answer: 248 girls

4 · Reviewdoes it hold up?

25 percent of 248 girls is 62 readers, which is 6 more than the boys' 56 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read less, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 7 medium

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $250$ boys in all, and $6$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

250 boys are split by hobby, 28 percent of them reading. The girls' graph gives reading 25 percent, and 6 more girls than boys read. We want the number of girls.

Givens

There are 250 boys.
Reading is 28 percent of the boys and 25 percent of the girls.
6 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

28 percent and 25 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

28 percent of the 250 boys.

250 \times 0.28 = 70

70 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

6 more than the boys.

70 + 6 = 76

76 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 76 girls are 25 percent of all the girls.

\text{girls} \times 0.25 = 76

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

76 \div 0.25 = 304

There are 304 girls.

Answer: 304 girls

4 · Reviewdoes it hold up?

25 percent of 304 girls is 76 readers, which is 6 more than the boys' 70 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read less, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 8 medium

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $250$ boys in all, and $12$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

250 boys are split by hobby, 20 percent of them reading. The girls' graph gives reading 25 percent, and 12 more girls than boys read. We want the number of girls.

Givens

There are 250 boys.
Reading is 20 percent of the boys and 25 percent of the girls.
12 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

20 percent and 25 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

20 percent of the 250 boys.

250 \times 0.2 = 50

50 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

12 more than the boys.

50 + 12 = 62

62 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 62 girls are 25 percent of all the girls.

\text{girls} \times 0.25 = 62

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

62 \div 0.25 = 248

There are 248 girls.

Answer: 248 girls

4 · Reviewdoes it hold up?

25 percent of 248 girls is 62 readers, which is 12 more than the boys' 50 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read more, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 9 hard

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $300$ boys in all, and $25$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

300 boys are split by hobby, 32 percent of them reading. The girls' graph gives reading 25 percent, and 25 more girls than boys read. We want the number of girls.

Givens

There are 300 boys.
Reading is 32 percent of the boys and 25 percent of the girls.
25 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

32 percent and 25 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

32 percent of the 300 boys.

300 \times 0.32 = 96

96 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

25 more than the boys.

96 + 25 = 121

121 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 121 girls are 25 percent of all the girls.

\text{girls} \times 0.25 = 121

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

121 \div 0.25 = 484

There are 484 girls.

Answer: 484 girls

4 · Reviewdoes it hold up?

25 percent of 484 girls is 121 readers, which is 25 more than the boys' 96 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read less, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 10 hard

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $400$ boys in all, and $7$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

400 boys are split by hobby, 38 percent of them reading. The girls' graph gives reading 30 percent, and 7 more girls than boys read. We want the number of girls.

Givens

There are 400 boys.
Reading is 38 percent of the boys and 30 percent of the girls.
7 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

38 percent and 30 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

38 percent of the 400 boys.

400 \times 0.38 = 152

152 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

7 more than the boys.

152 + 7 = 159

159 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 159 girls are 30 percent of all the girls.

\text{girls} \times 0.3 = 159

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

159 \div 0.3 = 530

There are 530 girls.

Answer: 530 girls

4 · Reviewdoes it hold up?

30 percent of 530 girls is 159 readers, which is 7 more than the boys' 152 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read less, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 11 hard

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $500$ boys in all, and $12$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

500 boys are split by hobby, 24 percent of them reading. The girls' graph gives reading 25 percent, and 12 more girls than boys read. We want the number of girls.

Givens

There are 500 boys.
Reading is 24 percent of the boys and 25 percent of the girls.
12 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

24 percent and 25 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

24 percent of the 500 boys.

500 \times 0.24 = 120

120 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

12 more than the boys.

120 + 12 = 132

132 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 132 girls are 25 percent of all the girls.

\text{girls} \times 0.25 = 132

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

132 \div 0.25 = 528

There are 528 girls.

Answer: 528 girls

4 · Reviewdoes it hold up?

25 percent of 528 girls is 132 readers, which is 12 more than the boys' 120 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read more, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Variant 12 hard

The circle graphs show the hobbies of the sixth-grade boys and girls at Jiwoo's school. There are $500$ boys in all, and $6$ more girls than boys give reading as their hobby. How many girls are there in all?

Your answer

Show solution

1 · Understandwhat's really being asked

500 boys are split by hobby, 22 percent of them reading. The girls' graph gives reading 20 percent, and 6 more girls than boys read. We want the number of girls.

Givens

There are 500 boys.
Reading is 22 percent of the boys and 20 percent of the girls.
6 more girls than boys give reading as their hobby.

Unknowns

The total number of girls.

Constraints

The two graphs describe different groups, so their percentages are not on the same base.

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #13 Convert to Algebra#8 Analyze the Units

22 percent and 20 percent sit on different totals and cannot be compared. Counts can. Turn the boys' percentage into a count, add the gap to get the girls' count, and let that count name the girls' total.

3 · Execute4 carry out the plan

1Count the boys who read

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

22 percent of the 500 boys.

500 \times 0.22 = 110

110 boys read.

2Count the girls who read

#15 Organize Information in More Ways 7.RP.A.3

6 more than the boys.

110 + 6 = 116

116 girls read.

3Use that as a share of the girls

#13 Convert to Algebra 6.EE.B.7

Those 116 girls are 20 percent of all the girls.

\text{girls} \times 0.2 = 116

One equation, one unknown.

4Solve for the total

#13 Convert to Algebra 6.EE.B.7

Divide by the share.

116 \div 0.2 = 580

There are 580 girls.

Answer: 580 girls

4 · Reviewdoes it hold up?

20 percent of 580 girls is 116 readers, which is 6 more than the boys' 110 -- both conditions hold.

Another way: Comparing the percentages directly would say girls read less, but a percentage is not a count until the group size is known.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Turning each group's percentage into a count.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the unknown total from a known share.

💡Takeaway. Two percentages of two different groups say nothing to each other. Counts do.

Percentages of different groups compare only through counts · 12 practice problems

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