Question

Find three consecutive odd integers whose sum is 13 more than twice the largest of the three integers.

Answer 1

15, 17, 19

Explanation:

Three consecutive odd integers can be represented by

x, x + 2, x + 4. You add 2 to each one to get the next one. Fun fact: you would do the same thing if the problem said the integers were even!

The largest integer is x + 4, so the sentence in the problem translates to an equation (sum means to add the integers together):

x + (x + 2) + (x + 4) = 2(x + 4) + 13

Distribute the 2, then combine like terms.

x + (x + 2) + (x + 4) = 2x + 8 + 13

3x + 6 = 2x + 21

Subtract 2x.

x + 6 = 21

Subtract 6.

x = 15

The integers requested are 15, 17, 19.

Check: Their sum is 51, which is 13 more than twice 19.