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Amanda and Todd purchase candy, popcorn, and pretzels at the

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Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink] Amanda and Todd purchase candy, popcorn, and pretzels at the   Updated on: 12 Dec 2012, 09:33
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Amanda and Todd purchase candy, popcorn, and pretzels at the stadium. If a package of candy costs half as much as a bag of popcorn, how much more money did Amanda and Todd spend on the candy than on the popcorn and pretzels combined?

(1) The cost of a bag of popcorn is equal to the cost of a pretzel.
(2) Amanda and Todd purchased 24 packages of candy, 6 pretzels, and 6 bags of popcorn.
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C

Originally posted by daviesj on 12 Dec 2012, 09:30.
Last edited by Bunuel on 12 Dec 2012, 09:33, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink] Amanda and Todd purchase candy, popcorn, and pretzels at the   12 Dec 2012, 09:48
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Amanda and Todd purchase candy, popcorn, and pretzels at the stadium. If a package of candy costs half as much as a bag of popcorn, how much more money did Amanda and Todd spend on the candy than on the popcorn and pretzels combined?

ITEM ------- # OF ITEMS PURCHASED ------- PRICE PER ITEM
Candy ----------------------- a ---------------------------- x
Popcorn --------------------- b ---------------------------- 2x (since a package of candy costs half as much as a bag of popcorn)
Pretzels --------------------- c ---------------------------- z

Question: \(ax-(2bx+cz)=?\)

(1) The cost of a bag of popcorn is equal to the cost of a pretzel --> \(2x=z\) --> substitute in the question: \(ax-(2bx+2cx)=x(a-2b-2c)=?\). Not sufficient.

(2) Amanda and Todd purchased 24 packages of candy, 6 pretzels, and 6 bags of popcorn --> \(a=24\) and \(b=c=6\). Not sufficient.

(1)+(2) Substitute the values from (2) into (1): \(x(a-2b-2c)=x(24-12-12)=0\), thus Amanda and Todd spent equal amount of money on the candy AND on the popcorn and pretzels combined. Sufficient.

Answer: C.
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink] Amanda and Todd purchase candy, popcorn, and pretzels at the   13 Dec 2012, 00:33
this was a tricky question... I marked 'E' cuz I thought as prices have not been given so info is incomplete
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink] Amanda and Todd purchase candy, popcorn, and pretzels at the   13 Dec 2012, 00:53
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Bunuel wrote:
Amanda and Todd purchase candy, popcorn, and pretzels at the stadium. If a package of candy costs half as much as a bag of popcorn, how much more money did Amanda and Todd spend on the candy than on the popcorn and pretzels combined?

ITEM ------- PRICE PER ITEM ------- # OF ITEMS PURCHASED
Candy --------------- a ---------------------------- x
Popcorn ------------- b ---------------------------- 2x (since a package of candy costs half as much as a bag of popcorn)
Pretzels ------------- c ---------------------------- z

Question: \(ax-(2bx+cz)=?\)

(1) The cost of a bag of popcorn is equal to the cost of a pretzel --> \(2x=z\) --> substitute in the question: \(ax-(2bx+2cx)=x(a-2b-2c)=?\). Not sufficient.

(2) Amanda and Todd purchased 24 packages of candy, 6 pretzels, and 6 bags of popcorn --> \(a=24\) and \(b=c=6\). Not sufficient.

(1)+(2) Substitute the values from (2) into (1): \(x(a-2b-2c)=x(24-12-12)=0\), thus Amanda and Todd spent equal amount of money on the candy AND on the popcorn and pretzels combined. Sufficient.

Answer: C.


Hi Bunuel.
I am a bit confused over the usage of words in the questions.
The question explicitly states that "a package of candy costs half as much as a bag of popcorn" then shouldn't a=b/2 rather than #of bags of candies=half of the #of bags of popcorn.
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink] Amanda and Todd purchase candy, popcorn, and pretzels at the   13 Dec 2012, 03:35
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Marcab wrote:
Bunuel wrote:
Amanda and Todd purchase candy, popcorn, and pretzels at the stadium. If a package of candy costs half as much as a bag of popcorn, how much more money did Amanda and Todd spend on the candy than on the popcorn and pretzels combined?

ITEM ------- PRICE PER ITEM ------- # OF ITEMS PURCHASED
Candy --------------- a ---------------------------- x
Popcorn ------------- b ---------------------------- 2x (since a package of candy costs half as much as a bag of popcorn)
Pretzels ------------- c ---------------------------- z

Question: \(ax-(2bx+cz)=?\)

(1) The cost of a bag of popcorn is equal to the cost of a pretzel --> \(2x=z\) --> substitute in the question: \(ax-(2bx+2cx)=x(a-2b-2c)=?\). Not sufficient.

(2) Amanda and Todd purchased 24 packages of candy, 6 pretzels, and 6 bags of popcorn --> \(a=24\) and \(b=c=6\). Not sufficient.

(1)+(2) Substitute the values from (2) into (1): \(x(a-2b-2c)=x(24-12-12)=0\), thus Amanda and Todd spent equal amount of money on the candy AND on the popcorn and pretzels combined. Sufficient.

Answer: C.


Hi Bunuel.
I am a bit confused over the usage of words in the questions.
The question explicitly states that "a package of candy costs half as much as a bag of popcorn" then shouldn't a=b/2 rather than #of bags of candies=half of the #of bags of popcorn.


Columns had wrong labels (PRICE PER ITEM and # OF ITEMS PURCHASED should have been reversed). Edited.
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink] Amanda and Todd purchase candy, popcorn, and pretzels at the   13 Dec 2012, 06:07
The problem I found with the question is whether bag and package are same or not.
In that case I marked E but when I re read the question I just got confused.
though option 1 seems a bit way ward and unclear.
answer would be C in case the the cost of bag of popcorn is equal to the cost of bag of pretzel.
option 1 is not clear as such
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink] Amanda and Todd purchase candy, popcorn, and pretzels at the   14 Dec 2012, 08:16
Nice question n nice explaination too...thnks
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink] Amanda and Todd purchase candy, popcorn, and pretzels at the   12 Nov 2022, 03:36
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink]
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