The sum of two numbers is 126. The difference of the same two numbers is 52. What is the higher of the two numbers?

Question

 write and solve a system of linear equations that represent the scenario. 

Answer 1

Let the 2 numbers be x and y.

 

x + y = 126

x - y = 52

 

Get x = y + 52 from the bottom equation, and substitute into the top equation to solve for y:

 

(y + 52) + y = 126

 

y = (126 - 52)/2 = 37

 

Now substitute this value of y into either equation to find x.  From the top equation,

 

x + 37 = 126

 

x = 126 - 37 = 89

 

Test the solution.