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?
m= microwave
r= refrigerator
s= savings
m+r=5/8s
r=4/7 x 5/8s=5/14s
r=5/14s
m=r-280
m=5/14s-280
m + r = 5/8s
5/14s-280 + 5/14= 5/8s
5/14s+5/14s-5/8 = 280
10/112s = 280
s= 280x112/10
s= savings = $3,136
answer = $3,136
To solve this problem, let's break it down step by step:
1. Let's say Madison's initial savings is represented by the variable "S."
2. We are given that she spent 5/8 of her savings on a microwave oven and a refrigerator. So, the amount she spent on the appliances is 5/8 * S.
3. We also know that she used 4/7 of the amount she spent to buy the refrigerator. Therefore, the cost of the refrigerator is 4/7 * (5/8 * S).
4. The problem states that the refrigerator cost $280 more than the microwave oven. So, the cost of the refrigerator is equal to the cost of the microwave oven plus $280: 4/7 * (5/8 * S) = (1/7 * (5/8 * S)) + $280.
5. Simplifying the equation, we have 4/7 * (5/8 * S) = 1/7 * (5/8 * S) + $280.
6. To get rid of the denominators, we can multiply both sides of the equation by 56 (the least common multiple of 7 and 8): 56 * (4/7 * (5/8 * S)) = 56 * (1/7 * (5/8 * S)) + 56 * $280.
7. This simplifies to: 20S = 5S + 56 * $280.
8. Combining like terms, we have 15S = 56 * $280.
9. Solving for S, we divide both sides of the equation by 15: S = (56 * $280) / 15.
10. Evaluating the expression, we find that Madison's initial savings, S, is $1049.33 (rounded to the nearest cent).
Therefore, Madison started with $1049.33 in savings.
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