Problem
One item's count and share give the total
Two circle graphs give the hobby shares of boys and of girls. The number of boys is known, along with how many more girls than boys read. We need the number of girls.
RatiosExpressions
Your answer
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
30 boys give reading.
6.RP.A.3Organize Information In More Ways2STEP 2
Cross over to the girls
Six more girls than boys read, and that comparison is between counts, not percentages.
30 + 6 = 36
36 girls give reading.
6.RP.A.3Identify SubproblemsThe two graphs can only be compared through counts, not percents.
Why?
Each graph's percents are hundredths of its own group, so a percent on one graph and a percent on the other are pieces of different wholes.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
A count of students, on the other hand, means one student per unit on either graph, so counts from the two can be set side by side.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
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
There are 120 girls.
6.SP.B.4Work BackwardsAnswer
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