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

Use a ratio to split a percent between items

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

Ratios

Your answer

How to solve

Strategy Analyze the Units — The bar tells us how much is left for the two unlabelled sections; the ratio tells us how to cut that leftover in two. Neither fact alone is enough -- together they are.

1STEP 1

Find how much is left over

Take the three labelled sections off the whole bar.

100 - 42 - 13 - 5 = 40

2STEP 2

Split the leftover in the given ratio

A ratio of 5 : 3 means cutting the 40% into 8 equal pieces and giving 5 to one and 3 to the other.

5 + 3 = 8, 40 ÷ 8 = 5

3STEP 3

Count the pieces for each

Family clinics take five of those pieces and oriental clinics take three.

5 × 5 = 25, 5 × 3 = 15

Answer

Family clinics 25%, oriental clinics 15%

Add all five back: 42 + 25 + 15 + 13 + 5 = 100, and 25 : 15 reduces to 5 : 3, so both conditions hold.

Takeaway

A ratio says how to cut something up, but not how big it is -- you need both.

Find how much is left over
Split the leftover in the given ratio
Count the pieces for each

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