algebra word problem

Question

Find two numbers whose difference is 10 and 1/6 of whose sum is 11.

Answer 1

Let the two numbers be x and y

 

x - y = 10

 

 

(x + y)/6 = 11

x + y = 66

x = 66 - y

 

 

x - y = 10

(66-y) - y = 10

66- y - y = 10

66 - 2y = 10

2y = 66-10

2y = 56

y = 56/2

y = 28

 

 

x = 66 - y

= 66 - 28

= 38

 

so the two numbers are 38 and 28