Mystery 2-digit numbers and systems of linear equations in three variables

by John
(UK)

2-digit numbers

There are three boxes to be added together to get 87.

The first box is ten more than the second and the
second is ten more than the third.


_ + _ + _ = 87


Let x be the first number

Let y be the second number

Let z be the third number

Then, we get the following 3 equations

x + y + z = 87 (1)

x = y + 10 (2)

y = z + 10 (3)

Using (3), we get z = y - 10

Substitute y - 10 for z and y + 10 for x in (1)

y + 10 + y + y - 10 = 87

3y = 87

y = 29

z = y - 10 = 29 - 10 = 19

x = y + 10 = 29 + 10 = 39


Therefore, 39 + 29 + 19 = 87