The difference of two numbers is 16. The greater number is 5 less than 4 times the smaller number. Find the two numbers.

Question

For this problem, identify your variables (define), set up a system of equations (2 equations, 2 variables), and then solve the system. State your answer in terms of the problem. Example:

The sum of two numbers is 92. Their difference is 20. Find the two numbers.

x = first number

y = second number

{x + y = 92

{x - y = 20

Answer 1

L-S = 16

L=4S-5

L= the greater number

S = the smaller number

L=16+S

16+S = 4S-5

3S =21

S = 21/3 = 7 = the smaller number

L =7+16 = 23 = the larger number

23= 4(7)-5 = 28-5 = 23

x+y= 92

x-y =20

2x =112

x = 56

y =92-56 = 36

56-36 = 20