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06 Dec 2021, 05:51
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Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, \($12\) on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?
A. \(60\)
B. \(66\)
C. \(72\)
D. \(78\)
E. \(84\)
A. \(60\)
B. \(66\)
C. \(72\)
D. \(78\)
E. \(84\)
06 Dec 2021, 05:51
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Official Solution:
Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, \($12\) on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?
A. \(60\)
B. \(66\)
C. \(72\)
D. \(78\)
E. \(84\)
Let the amount Luis spent in the supermarket be \($x\).
Luis spent a third of the money on fruits \(=\frac{x}{3}\);
Luis spent a sixth of the money on vegetables \(=\frac{x}{6}\);
Luis spent \($12\) of the money on pasta \(=12\);
Luis spent half the remainder of the money on chocolate \(=(x-(\frac{x}{3}+\frac{x}{6}+12))*\frac{1}{2}=\frac{x}{4}-6\);
Luis spent s much on soda as he spent on vegetables \(=\frac{x}{6}\).
So, we have that \(\frac{x}{3}+\frac{x}{6}+12+(\frac{x}{4}-6)+\frac{x}{6}=x\);
\(x=72\).
Answer: C
Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, \($12\) on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?
A. \(60\)
B. \(66\)
C. \(72\)
D. \(78\)
E. \(84\)
Let the amount Luis spent in the supermarket be \($x\).
Luis spent a third of the money on fruits \(=\frac{x}{3}\);
Luis spent a sixth of the money on vegetables \(=\frac{x}{6}\);
Luis spent \($12\) of the money on pasta \(=12\);
Luis spent half the remainder of the money on chocolate \(=(x-(\frac{x}{3}+\frac{x}{6}+12))*\frac{1}{2}=\frac{x}{4}-6\);
Luis spent s much on soda as he spent on vegetables \(=\frac{x}{6}\).
So, we have that \(\frac{x}{3}+\frac{x}{6}+12+(\frac{x}{4}-6)+\frac{x}{6}=x\);
\(x=72\).
Answer: C
knowledgeispowerr
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07 Oct 2023, 12:59
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I think this is really unclear because it would be logical to think that the remainder includes the soda. i dont think the question is worded clearly sorry
