Question

The sum of three numbers is 10. Two times the second number minus the first number is equal to 12. The first number minus the second number plus twice the third number equals 7. Find the numbers

Answer 1

x = -2, y = 5, z = 7

Explanation:

Let these 3 numbers be x, y, and z

x is the first

y is the second

z is the third number.

Then:

x + y + z = 10

2*y - x = 12

x - y + 2z = 7

x = 2y - 12

(2y - 12) + y + z = 10

and

(2y - 12) - y + 2z = 7

so

3y + z = 22

y + 2z = 19

y = 19 - 2z

3*(19 - 2z) + z = 22

57 - 6z + z = 22

57 - 5z = 22

35 = 5z

z = 7

y = 19 - 2*7 = 19 - 14 = 5

x = 2y - 12 = 2*5 -12 = 10 -12 = -2