Data & Graphs

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

A percent gap plus a count gap gives the total

The circle graph at the right shows which foreign language students at Yeona's school want to learn. There are 88 more students who want Chinese than students who want Japanese. How many students want to learn German?

Share of students by the foreign language they want to learn English (40%) Chinese (30%) Japanese (20%) German (5%) Other (5%)
RatiosExpressions
Your answer
How to solve
Strategy Work Backwards — Every percent on the graph is measured against the same total, so the gap between two of them is a percent of that same total. That one sentence hands back the total, and everything else follows.
1STEP 1

Turn the gap into a percent

Both shares are measured against the same total, so their difference is a share of that total too.

30 - 20 = 10
2STEP 2

Use the gap to find the total

That 10% is 8 students, so the whole school is ten times as many.

8 ÷ 10 × 100 = 80
3STEP 3

Take the German share of it

German is 5% of the total just found.

80 × 0.05 = 4
Answer
4 students
Count the two languages directly: Chinese is 24 students and Japanese is 16, a gap of 8 exactly as stated.
Takeaway

A difference between two shares of the same whole is itself a share of that whole.

  • Turn the gap into a percent
  • Use the gap to find the total
  • Take the German share of it
Where next?
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