   SEARCH HOME Math Central Quandaries & Queries  Question from Shawna, a student: You are told that you are working with three different numbers. When the first number is added to twice the other two numbers, the result s 64( i.e x+2y+2z= 64). When the second number is added to twice the other two numbers the result is 62 (y+2x+2z=62). Finally, when the third number is added to twice the other two numbers, the result is 59 (z+2x+2y=59) Determine the three numbers? Hi Shawna,

You have

x + 2y + 2z = 64            (1)
2x + y + 2z = 62            (2)
2x + 2y + z = 59            (3)

The first thing that I notice about these three equations is that if you add all three together then on the left side you get

5(x + y + z)

and on the right side

64 + 62 + 59 = 185

thus

x + y + z = 37            (4)

Now subtract equation (2) from equation (1) to get -x + y = 2 or

x = y - 2            (5)

Then subtract equation (3) from equation (2) to get -y + z = 3 or

z = y + 3            (6)

Substitute equations (5) and (6) into equation (4) and solve for y.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.