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# A sporting goods store sold 64 Frisbees in one week, some for \$3 and

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Joined: 02 Sep 2009
Posts: 58340
A sporting goods store sold 64 Frisbees in one week, some for \$3 and  [#permalink]

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17 Jan 2016, 11:58
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Difficulty:

35% (medium)

Question Stats:

77% (02:05) correct 23% (02:00) wrong based on 127 sessions

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A sporting goods store sold 64 Frisbees in one week, some for \$3 and the rest for \$4 each. If receipts from Frisbee sales for the week totaled \$204, what is the fewest number of \$4 Frisbees that could have been sold?

A. 24
B. 12
C. 8
D. 4
E. 2

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Re: A sporting goods store sold 64 Frisbees in one week, some for \$3 and  [#permalink]

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19 Jan 2016, 12:46
The wording of the question is slightly misleading. When a question asks what is the fewest that could have been sold, it is suggesting that there could be many different quantities sold.

In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly \$204, there is only one possible solution for the number of \$3 and \$4 Frisbees sold.

To solve, we have 2 equations and 2 unknowns
Let x = number of \$3 Frisbees sold
Let y = number of \$4 Frisbees sold

x + y = 64
3x + 4y = 204

x = 64 - y
3(64-y) + 4y = 204
192 - 3y + 4y = 204
y = 12

If we were NOT told how many Frisbees were sold in total, then the question would make more sense for the way it was worded. In that case, we would want to find the smallest number y, that when 4y is subtracted from 204, leaves a multiple of 3. Since 204 is itself a multiple of 3, we would need a number of \$4 Frisbees that resulted in sales that were a multiple of 3 also. I.e. 4y = multiple of 3. Looking at the answer choices, the smallest number y that works is 12.

Another good method to find that answer would be to plug in the answer choices starting with the smallest.

E) 204 - 4*2 = 196 --> not a multiple of 3
D) 204 - 4*4 = 188 --> not a multiple of 3
C) 204 - 4*8 = 172 --> not a multiple of 3
B) 204 - 4*12 = 156 --> multiple of 3

Note: In my scenario, the fewest number of \$3 Frisbees that could have been sold is actually 0. The question would have had to specify that at least one \$4 Frisbee was sold for the answer to be B.
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Dave de Koos
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Re: A sporting goods store sold 64 Frisbees in one week, some for \$3 and  [#permalink]

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02 Jan 2019, 20:29
davedekoos wrote:
The wording of the question is slightly misleading. When a question asks what is the fewest that could have been sold, it is suggesting that there could be many different quantities sold.

In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly \$204, there is only one possible solution for the number of \$3 and \$4 Frisbees sold.

To solve, we have 2 equations and 2 unknowns
Let x = number of \$3 Frisbees sold
Let y = number of \$4 Frisbees sold

x + y = 64
3x + 4y = 204

x = 64 - y
3(64-y) + 4y = 204
192 - 3y + 4y = 204
y = 12

If we were NOT told how many Frisbees were sold in total, then the question would make more sense for the way it was worded. In that case, we would want to find the smallest number y, that when 4y is subtracted from 204, leaves a multiple of 3. Since 204 is itself a multiple of 3, we would need a number of \$4 Frisbees that resulted in sales that were a multiple of 3 also. I.e. 4y = multiple of 3. Looking at the answer choices, the smallest number y that works is 12.

Another good method to find that answer would be to plug in the answer choices starting with the smallest.

E) 204 - 4*2 = 196 --> not a multiple of 3
D) 204 - 4*4 = 188 --> not a multiple of 3
C) 204 - 4*8 = 172 --> not a multiple of 3
B) 204 - 4*12 = 156 --> multiple of 3

Note: In my scenario, the fewest number of \$3 Frisbees that could have been sold is actually 0. The question would have had to specify that at least one \$4 Frisbee was sold for the answer to be B.

I would be careful when it comes to the last bit:

In my scenario, the fewest number of \$3 Frisbees that could have been sold is actually 0. The question would have had to specify that at least one \$4 Frisbee was sold for the answer to be B

We cant forget that only 64 frisbees were sold.
Re: A sporting goods store sold 64 Frisbees in one week, some for \$3 and   [#permalink] 02 Jan 2019, 20:29
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