The ratio of the amount of money Bill had to his sister Haley was 5:6. Haley spent $42 on a new pair of shoes, and now Bill has twice as much money as his sister. How much money does Bill have? How much money did the two of them start out with combined?
Let
x -----> the amount of money Bill had
y -----> the amount of money Haley had
we have that
x/y=5/6 ------> x=(5/6)y -----> equation 1
x=2(y-42) -----> x=2y-84 -----> equation 2
solve the system of equations
Equate both equations
(5/6)y=2y-84
solve for y
Multiply by 6 both sides
5y=12y-504
12y-5y=504
7y=504
y=72
Find out the value of x
x=(5/6)(72)
x=60
therefore
Billy have $60
and
them combined start with (60+72)=$132