Sally bought a dress, a shirt and a wallet at a sale. She could have bought one more similar dress if she did not buy the shirt and the wallet. 3-5 of the price of the dress was equivalent to twice the price of the wallet. (a) What was the ratio of the price of the dress to the price of the shirt to the price of the wallet? (b) If the shirt cost $32 more than the wallet, how much did the dress cost?
Question
Sally bought a dress, a shirt and a wallet at a sale. She could have bought one more similar dress if she did not buy the shirt and the wallet. 3-5 of the price of the dress was equivalent to twice the price of the wallet. (a) What was the ratio of the price of the dress to the price of the shirt to the price of the wallet? (b) If the shirt cost $32 more than the wallet, how much did the dress cost?
Solution
(a) Let's denote the price of the dress as D, the price of the shirt as S, and the price of the wallet as W.
From the problem, we know that:
- D = S + W (Sally could have bought one more dress if she did not buy the shirt and the wallet)
- 3/5 * D = 2 * W (3/5 of the price of the dress was equivalent to twice the price of the wallet)
We can substitute the first equation into the second to get:
3/5 * (S + W) = 2 * W 3/5 * S + 3/5 * W = 2 * W 3/5 * S = 2 * W - 3/5 * W 3/5 * S = 7/5 * W
So, the ratio of the price of the dress to the price of the shirt to the price of the wallet is 5:3:7.
(b) We know that S = W + $32. Substituting this into the first equation gives:
D = W + 32
And from the second equation, we know that 3/5 * D = 2 * W. Substituting this into the equation above gives:
3/5 * D = D - 32 D = 80
So, the dress cost $80.
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