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Double Trouble

What number can you add to 129 and subtract from 129 such that the sum of the number and 129 is twice the difference between 129 and the number?

Solution

We are looking for the value of N.

Let's establish some number sentences reflecting the information given:

The sum of 129 and N can be denoted as X.

N + 129 = X

The difference between 129 and N can be denoted as Y.

129 - N = Y

The problem states that the sum of the number and 129 is twice the difference between 129 and the number. That can be expressed in this way:

N + 129 = 2(129 - N)

N + 129 = 258 - 2N

3N = 129

N = 43

Now let's double check our answer!

By substituting 43 for N, we have:

43 + 129 = 172

129 - 43 = 86

86 x 2 = 172

Therefore, 43 indeed equals N!