Operations & Word Problems

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

Reduce the investment ratio to whole numbers

Emma invested $150 and Noah invested $200, and they split the profit in the ratio of what they invested. The total profit is $70. We need Emma's share.
Ratios
Your answer
How to solve
Strategy Analyze the Units — Simplify the ratio first and the big numbers stop mattering: the profit is cut into as many equal parts as the two terms add to, and each person takes their own number of parts.
1STEP 1

Simplify the ratio of the investments

Both amounts are multiples of $50.

150 ÷ 50 = 3, 200 ÷ 50 = 4
2STEP 2

Count the equal parts

The two terms tell how many parts the profit is cut into altogether.

3 + 4 = 7
3STEP 3

Take Emma's parts

Emma gets three of the seven parts of the profit.

70 ÷ 7 = 10, 10 × 3 = 30
Answer
$30
Check the other share: Noah gets 10 × 4 = 40 dollars, and 30 + 40 = 70 dollars.
Takeaway

Sharing in a ratio means cutting into as many equal parts as the terms add to.

  • Simplify the ratio of the investments
  • Count the equal parts
  • Take Emma's parts
Where next?
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Write the rate as a fraction to read off both termsChain two ratios, then evaluate by ratios

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▶ Practice — 12 problems