The sum of two positive numbers is 5 times their difference. What is the ratio of the larger number to the smaller number?

Let the numbers be n and m, with n > m

 

n + m = 5(n - m)

 

Distribute the 5 on the right

n + m = 5n - 5m

 

Add 5m to both sides

n + 6m = 5n

 

Subtract n from both sides

6m = 4n

 

Divide both sides by 4

1.5m = n

 

Divide both sides by m

1.5 = n/m

 

or n/m = 1.5.    This is the ratio of the larger number to the smaller.