Question

Harry earns $45 a week more than Xena. George earns $18 a week less than Xena. If Harry earns the same amount in two weeks that George earns in three weeks, how much money does Xena earn a week?

Answer 1

Answer:

Xena earns $144 per a week.

Step-by-step explanation:

Harry earns - $ h

Xena earns - $ x

George earns -$ g

Harry earns $45 a week more than Xena.      h= x+45

George earns $18 a week less than Xena.     g = x - 18

If Harry earns the same amount in two weeks that George earns in three weeks

2h = 3g

So, we have the system of 3 equations:

h= x+45

g = x - 18

2h = 3g    (*)

Substitute values of h and g into equation (*)

2(x+45) = 3(x-18)

2x + 90 = 3x - 54

90+54 = 3x- 2x

x= 144