The larger of two numbers is 17 less than four times four times the smaller number. The sum of the two numbers is 78. Find the two numbers.

Question

The larger of two numbers is 17 less than four times four times the smaller number. The sum of the two numbers is 78. Find the two numbers.

 

 

How would I set up an equation for this?

 

Answer 1

Let the two numbers be x and y, with y > x.

 

Then from the problem statement,

 

y = 4x - 17

x + y = 78

 

You have a system of two equations in two unknowns x and y.  From the bottom equation, get

 

y = 78 - x

 

and substitute into the top equation to find x:

 

78 - x = 4x - 17

 

95 = 5x

 

x = 19

 

Then

 

y = 78 - x = 78 - 19 = 59

 

y = 59