math
posted by Tyler on .
Madison spent 5/8 of her savings on a microwave oven & a refrigerator. She used 4/7 of the amount she spent to buy the refrigerator. The refrigerator cost $280 more than the microwave oven. How much savings did Madison start with?

let the amount of her savings be x
cost of both = (5/8)x
cost of fridge = (4/7)(5/8)x = (5/14)x
(5/8)x  (5/14)x = 280
15x/56 = 280
15x = 15680
x = 1045.33
Here savings were $1053.33
cost of fridge = ((5/14)(1045.33 = 373.33
cost of both = (5/8)(1045.33) = 653.33
difference = 653.33  373.33 = 280
all checks out 
m= microwave
r= refrigerator
s= savings
m+r=5/8s
r=4/7 x 5/8s=5/14s
r=5/14s
m=r280
m=5/14s280
m + r = 5/8s
5/14s280 + 5/14= 5/8s
5/14s+5/14s5/8 = 280
10/112s = 280
s= 280x112/10
s= savings = $3,136