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29 Jul 2024, 04:06
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A boulangerie's cost for baking croissants is 0.60 euros for each of the first 100 croissants and 0.30 euros for each additional croissant after the first 100. On Sunday, the boulangerie baked and sold \(n\) croissants, where \(n > 100\), for 1.5 euros each. If the profit on selling these croissants was 200%, what is the value of \(n\)?
A. 125
B. 150
C. 175
D. 200
E. 400
A. 125
B. 150
C. 175
D. 200
E. 400
29 Jul 2024, 04:06
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Official Solution:
A boulangerie's cost for baking croissants is 0.60 euros for each of the first 100 croissants and 0.30 euros for each additional croissant after the first 100. On Sunday, the boulangerie baked and sold \(n\) croissants, where \(n > 100\), for 1.5 euros each. If the profit on selling these croissants was 200%, what is the value of \(n\)?
A. 125
B. 150
C. 175
D. 200
E. 400
The cost for producing \(n\) croissants, where \(n > 100\), would be:
\(0.6*100 + 0.3(n - 100) =\)
\(= 60 + 0.3n - 30 =\)
\(= 30 + 0.3n\).
The profit for selling \(n\) croissants, at 1.5 euros each, would be:
\(Profit = Revenue - Cost =\)
\(= 1.5n - (30 + 0.3n) =\)
\(= 1.2n - 30\).
The profit of 200% would imply that:
\(\frac{Profit}{Cost} = \frac{200}{100}\)
\(\frac{1.2n - 30}{30 + 0.3n} = 2\)
\(1.2n - 30 = 60 + 0.6n\)
\(0.6n = 90\)
\(n = 150\).
Answer: B
A boulangerie's cost for baking croissants is 0.60 euros for each of the first 100 croissants and 0.30 euros for each additional croissant after the first 100. On Sunday, the boulangerie baked and sold \(n\) croissants, where \(n > 100\), for 1.5 euros each. If the profit on selling these croissants was 200%, what is the value of \(n\)?
A. 125
B. 150
C. 175
D. 200
E. 400
The cost for producing \(n\) croissants, where \(n > 100\), would be:
\(0.6*100 + 0.3(n - 100) =\)
\(= 60 + 0.3n - 30 =\)
\(= 30 + 0.3n\).
The profit for selling \(n\) croissants, at 1.5 euros each, would be:
\(Profit = Revenue - Cost =\)
\(= 1.5n - (30 + 0.3n) =\)
\(= 1.2n - 30\).
The profit of 200% would imply that:
\(\frac{Profit}{Cost} = \frac{200}{100}\)
\(\frac{1.2n - 30}{30 + 0.3n} = 2\)
\(1.2n - 30 = 60 + 0.6n\)
\(0.6n = 90\)
\(n = 150\).
Answer: B
12 Nov 2024, 23:40
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The question does not clarify clearly about profit percentage base, which can be revenue or cost.
