The sum of two numbers is 72.  One of the numbers is six more than twice the other.  What are the two numbers?


Let one number be x, and the other be y.

The sum of two numbers is 72   ------   x+y = 72

One of the numbers is six more than twice the other.  ---   x = 2y + 6

We have a pair of simultaneous equations, which we can solve.

x+y = 72....(1)
x = 2y + 6....(2)

Substitute (2) into (1):

(2y + 6) + y = 72

3y + 6 = 72

3y = 66

y = 22...(3)

Subsitute (3) into (2):

x = 2(22) + 6 = 50

Hence, our two numbers are 50,22.