Fractions & Decimals

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

Population density is people over area

Eunwoo's village is 1 km21\ \text{km}^2 larger in area than Hyuntae's. Eunwoo's village has 195195 people and Hyuntae's has 160160. If the population per unit area in Hyuntae's village is 8080, find the population per unit area in Eunwoo's.

Ratios
Your answer
How to solve
Strategy Analyze the Units — The rate we want needs an area we do not have. But the other village's rate hands back its area, and the two areas are linked -- so go the long way round rather than looking for a shortcut.
1STEP 1

Get Hyuntae's area from his rate

The rate is population divided by area, so area is population divided by the rate.

160 ÷ 80 = 2
2STEP 2

Step across to Eunwoo's area

Eunwoo's village is 1 km² larger.

2 + 1 = 3
3STEP 3

Work out Eunwoo's rate

Divide his village's population by the area just found.

195 ÷ 3 = 65
Answer
65
Check it forwards: 65 × 3 = 195 people, and 80 × 2 = 160 people -- both villages come back out right.
Takeaway

When the rate you want needs a missing quantity, look for another rate that hands it back.

  • Get Hyuntae's area from his rate
  • Step across to Eunwoo's area
  • Work out Eunwoo's rate
Where next?
Level upsuggested
Scale a simple ratio up to bigger numbersScaling both terms keeps the ratio
Another one like thissuggested
12 practice problems
Step back and solidifysuggested
A rate is the ratio written as a numberA percent is a rate out of 100

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▶ Practice — 12 problems