Solve word problems using guess-and-check

Learn with an example

✈️ Carla bought a box with both chocolate and maple doughnuts. There were 2 fewer maple doughnuts than chocolate doughnuts, and there were 12 doughnuts in all.

How many chocolate doughnuts did Carla buy?

________chocolate doughnuts

solution:

  • You need to find two numbers whose sum is 12 and whose difference is 2.
  • You need to find two numbers whose sum is 12 and whose difference is 2.
  • Think of pairs of numbers whose difference is 2. Then find the sum of each pair.
DifferenceSum
3 − 1 = 23 + 1 = 4
4 − 2 = 24 + 2 = 6
5 − 3 = 25 + 3 = 8
6 − 4 = 26 + 4 = 10
7 − 5 = 27 + 5 = 12
8 − 6 = 28 + 6 = 14
  • The numbers are 7 and 5. Carla bought 7 chocolate doughnuts and 5 maple doughnuts.

✈️ Amy bought a box with both chocolate and maple doughnuts. There were 7 fewer maple doughnuts than chocolate doughnuts, and there were 11 doughnuts in all.

How many chocolate doughnuts did Amy buy?

______chocolate doughnuts

solution:

  • You need to find two numbers whose sum is 11 and whose difference is 7.
  • Think of pairs of numbers whose difference is 7. Then find the sum of each pair.
DifferenceSum
8 − 1 = 78 + 1 = 9
9 − 2 = 79 + 2 = 11
10 − 3 = 710 + 3 = 13
11 − 4 = 711 + 4 = 15
12 − 5 = 712 + 5 = 17
  • The numbers are 9 and 2. Amy bought 9 chocolate doughnuts and 2 maple doughnuts.

✈️ The canteen sold 3 fewer bowls of chicken soup than bowls of tomato soup. They sold 17 bowls of soup in all.

How many bowls of chicken soup did the canteen sell?

__________bowls of chicken soup

solution:

  • You need to find two numbers whose sum is 17 and whose difference is 3.
  • Think of pairs of numbers whose difference is 3. Then find the sum of each pair.
DifferenceSum
5 − 2 = 35 + 2 = 7
6 − 3 = 36 + 3 = 9
7 − 4 = 37 + 4 = 11
8 − 5 = 38 + 5 = 13
9 − 6 = 39 + 6 = 15
10 − 7 = 310 + 7 = 17
  • The numbers are 10 and 7. The canteen sold 10 bowls of tomato soup and 7 bowls of chicken soup.

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