Depth · one concept from first principles · step 2 of 4

One item's count and share give the total

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?

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How to solve

Strategy Organize Information in More Ways — The two graphs have different bases, so percentages cannot be compared across them. Counts can. Go down to a count on the boys' side, cross over with the given difference, then climb back up on the girls' side.

1STEP 1

Count the boys who read

Reading is 20% of the 150 boys.

150 × 0.2 = 30

2STEP 2

Cross over to the girls

Six more girls than boys read, and that comparison is between counts, not percentages.

30 + 6 = 36

3STEP 3

Climb back to the total

Those 36 girls are 30% of all the girls, so divide by the share.

36 ÷ 30 × 100 = 120

Answer

120 girls

Check it forwards: 30% of 120 girls is 36, which is 6 more than the 30 boys.

Takeaway

Percentages from two different graphs cannot be compared -- drop down to counts first.

Count the boys who read
Cross over to the girls
Climb back to the total

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