Answer:
Part a) Wayne's savings before he spent $28 was $31.08
Part b) Stef's savings after she spent $28 was $9.29
Step-by-step explanation:
Part a)
Let
x ----> original amount of Wayne's savings
y ----> original amount of Stef's savings
we know that
Original ratio
[tex]\frac{x}{y}=\frac{5}{6}[/tex]
[tex]x=\frac{5}{6}y[/tex] ----> equation A
After spending $28 each
[tex]\frac{x-28}{y-28}=\frac{1}{4}[/tex]
Multiply in cross
[tex]4x-112=y-25\\y=4x-112+25[/tex]
[tex]y=4x-87[/tex] ----> equation B
substitute equation A in equation B
[tex]y=4(\frac{5}{6}y)-87[/tex]
solve for y
[tex]\frac{20}{6}y-y=87[/tex]
[tex]\frac{7}{3}y=87[/tex]
[tex]y=37.29[/tex]
Find the value of x
[tex]x=\frac{5}{6}(37.29)=31.08[/tex]
so
The original amount of Wayne's savings was $31.08 and the original amount of Stef's savings was $37.29
therefore
Wayne's savings before he spent $28 was $31.08
Part b) Find Stef's savings after she spent $28
Subtract $28 from the original savings
so
$37.29-$28=$9.29
therefore
Stef's savings after she spent $28 was $9.29
