Judy and Ramey together have 42 animals. Judy has 12 fewer animals than Ramey. How many stuffed animals does each girl have?
Solve by trial and error
Basically this means that you will look for 2 numbers that add up to 42 and one of the two numbers is bigger by 12.
If you choose 20 to be one of the numbers then, the other one is 20  12 = 8 or 20 + 12 = 32
20 and 8 don't add up to 42.
20 and 32 don't add up to 42 either.
This method look more like guessing.
What if I looked for all combinations of 2 numbers to add to get 42 and then choose the pair with a difference of 12.
42 = 41 + 1 difference is 40
42 = 40 + 2 difference is 38
42 = 39 + 3 difference is 36
42 = 38 + 4 difference is 34
42 = 37 + 5 difference is 32
42 = 36 + 6 difference is 30
42 = 35 + 7 difference is 28
42 = 34 + 8 difference is 26
42 = 33 + 9 difference is 24
42 = 32 + 10 difference is 22
42 = 31 + 11 difference is 20
42 = 30 + 12 difference is 18
42 = 29 + 13 difference is 16
42 = 28 + 14 difference is 14
42 = 27 + 15 difference is 12
Stop! You have found what you are looking for.
The numbers are 27 and 15
27  15 = 12
27 + 15 = 42
So Ramey has 27 stuffed animals and Judy has 15
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