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16 Sep 2014, 01:00
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Difficulty:
45%
(medium)
Question Stats:
73% (02:16) correct
27%
(02:06)
wrong
based on 84
sessions
History
Date
Time
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Not Attempted Yet
Albert sells chocolate ice cream at $0.15 per cup and vanilla ice cream at $0.14 per cup. If Albert earned $5 from his sales during the day, what is the minimum number of vanilla cups he could have sold?
A. 0
B. 5
C. 10
D. 15
E. 20
A. 0
B. 5
C. 10
D. 15
E. 20
16 Sep 2014, 01:00
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Official Solution:
Albert sells chocolate ice cream at $0.15 per cup and vanilla ice cream at $0.14 per cup. If Albert earned $5 from his sales during the day, what is the minimum number of vanilla cups he could have sold?
A. 0
B. 5
C. 10
D. 15
E. 20
Let \(c\) and \(v\) denote the number of chocolate ice creams and vanilla ice creams sold during the day. Note that both \(c\) and \(v\) must be integers since they represent the number of ice cream cups.
The question is: What is the least integer value for \(v\) such that \(0.15c + 0.14v = 5\)? Multiplying by 100 for simplification gives \(15c + 14v = 500\).
Observe that \(v\) must end with either 0 or 5; otherwise, \(15c + 14v\) will not result in a number with the units digit of 0, as 500 does.
\(v\) cannot be 0 because in this case \(c\) will not be an integer.
\(v\) cannot be 5 because in this case \(c\) will not be an integer.
However, \(v\) can be 10; in this case, \(c\) will be an integer, namely, 24.
Therefore, the minimum number of vanilla cups Albert could have sold is 10.
Answer: C
Albert sells chocolate ice cream at $0.15 per cup and vanilla ice cream at $0.14 per cup. If Albert earned $5 from his sales during the day, what is the minimum number of vanilla cups he could have sold?
A. 0
B. 5
C. 10
D. 15
E. 20
Let \(c\) and \(v\) denote the number of chocolate ice creams and vanilla ice creams sold during the day. Note that both \(c\) and \(v\) must be integers since they represent the number of ice cream cups.
The question is: What is the least integer value for \(v\) such that \(0.15c + 0.14v = 5\)? Multiplying by 100 for simplification gives \(15c + 14v = 500\).
Observe that \(v\) must end with either 0 or 5; otherwise, \(15c + 14v\) will not result in a number with the units digit of 0, as 500 does.
\(v\) cannot be 0 because in this case \(c\) will not be an integer.
\(v\) cannot be 5 because in this case \(c\) will not be an integer.
However, \(v\) can be 10; in this case, \(c\) will be an integer, namely, 24.
Therefore, the minimum number of vanilla cups Albert could have sold is 10.
Answer: C
20 Oct 2023, 09:40
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
