The ratio of two numbers is 4:5, and their sum is 108. What are their numbers?

Question

Please explain so I know how to do these :)

Answer 1

4x + 5x = 108

 

9x = 108

 

x = 108/9 = 12

 

12*4

12*5

 

48, 60

 

 

Answer 2

Let x and y be the two numbers;

 

Equation 1: x/y = 4/5 (from problem statement)

Equation 2: x + y = 108 (from problem statement)

 

From equation 2: x = 108 - y

 

Substitute x into equation 1, you get (108-y)/y = 4/5 

 

Multiply y on both sides you get, 108 - y = 4y/5

 

Multiply 5 on both sides you get, 108*5 - 5y = 4y

 

Add 5y to both sides you get, 540 = 9y

 

Solve for y = 540/9 = 60

 

Plug y into equation 2 you get, x + 60 = 108

 

Subtract 60 from both sides, you get x = 48. 

 

Thus the answers are 48 and 60.