Question

Three consecutive odd numbers are such that if you subtract the product of the smaller two from the product of the greater two, the result will be 76. Find these numbers.

Answer 1

17 19 21

Explanation:

Answer 2

37, 38, and 39

Explanation:

Write the equation by converting words into math symbols:

• consecutive means n, n+1, and n+2
• subtract -
• product *
• result is =

This means "the product of the smaller two" is n(n+1).

This also means "the product of the greater two" is (n+1)(n+2)

They are subtracted from each other and equal to 76. So it becomes

(n+1)(n+2) - n(n+1) = 76

Write and solve:

`(n+1)(n+2) - n(n+1) = 76\\n^2+n+2n+2-n^2-n=76\\n+2n+2-n=76\\2n+2=76\\2n=74\\n=37`

The smallest number is 37. The next is 38. The last is 39.