The difference between two numbers is 16. The smaller number is 9 less than three times the larger number. Find both numbers.

Question

The difference between two numbers is 16. The smaller number is 9 less than three times

the larger number. Find both numbers.

Answer 1

Let x be the bigger, y the smaller.

 

x - y = 16

 

y = 3x - 9

 

Solve this system of equations:

 

Add the two equations and get

 

x = 3x + 7

 

x = -7/2 = -3.5

 

y = x - 16 = -3.5 - 16 = -19.5

 

 

Answer 2

x - y = 16 (Equation 1)

 

x is the larger number because x - y is positive.

y is the smaller number

 

three times the larger number is 3x

9 less than three times the larger number is 3x-9

 

y = 3x - 9 (Equation 2)

 

substitute Equation 2 into Equation 1:

 

x - (3x-9) = 16

-2x + 9 = 16

-2x = 7

x = -3.5

 

y = 3x - 9 = -10.5 -9 = -19.5

 

Check your answer in Equation 1:

 

Does x - y = 16 ?

 

-3.5 - (-19.5) = -3.5 + 19.5 = 16  CORRECT