Question

Shane thinks of three integers. Added two at a time, their sums are 37, 41, and 44. What is the product of the three integers?

Answer 1

8160

Explanation:

Given the integers as x, y and z, then we have

x + y = 37 => y = 37 - x

x + z = 41 => z = 41 - x

y + z = 44 => (37 - x) + (41 - x) = 44

=> 78 - 2x = 44

=> 2x = 78 - 44 = 34

=> x = 34/2 = 17

y = 37 - x = 37 - 17 = 20

z = 41 - x = 41 - 17 = 24

The product of the three integers

= 17 x 20 x 24 = 8160