Operations & Word Problems

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

Moving some across leaves the total unchanged

Jia and Minho each had 2020 candies. After Jia gave some candies to Minho, the ratio of Jia's candies to Minho's became 1:31 : 3. How many candies did Jia give away?

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How to solve
Strategy Change Focus / Count the Complement — Moving candies between two people changes each amount but not their total, and the total is the one number the new ratio can be applied to. Find what Jia is left with, then compare it with what she started with.
1STEP 1

See that the total does not change

Candies only moved from one to the other, so the two amounts still add to the same number.

20 + 20 = 40
2STEP 2

Split the total in the new ratio

A ratio of 1 : 3 cuts the total into four equal parts, and Jia keeps one.

1 + 3 = 4, 40 ÷ 4 = 10
3STEP 3

Compare with what she started with

What she gave away is the difference between what she had and what she has left.

20 - 10 = 10
Answer
10 candies
Check the ratio: Jia has 10 and Minho has 20 + 10 = 30, and 10 : 30 is 1 : 3.
Takeaway

Moving things between two people changes each amount but never the total -- so work from the total.

  • See that the total does not change
  • Split the total in the new ratio
  • Compare with what she started with
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