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Every box of cookies contains exactly 6 cookies.
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04 Mar 2018, 13:52
04 Mar 2018, 13:52
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Question Stats:
36% (02:05) correct
63% (01:07) wrong based on 30 sessions
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Every box of cookies contains exactly 6 cookies.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The total number of cookies purchased if Sally purchased 3 more than twice as many boxes of oatmeal cookies as boxes of chocolate chip cookies |
The total number of cookies purchased if Sally purchased 2 fewer than 3 times as many boxes of oatmeal cookies as boxes of chocolate chip cookies |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Drill 1
Question: 16
Page: 496
Question: 16
Page: 496
Re: Every box of cookies contains exactly 6 cookies.
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04 Mar 2018, 14:27
04 Mar 2018, 14:27
Expert Reply
Explanation
First, plug in 1 for the number of boxes of chocolate chip cookies.
In Quantity A, if Sally buys 1 box of chocolate chip cookies, then she buys 2(1) + 3 = 5 boxes of oatmeal cookies, for a total of 6 boxes, or 36 cookies.
In Quantity B, if Sally buys 1 box of chocolate chip cookies, then she buys 3(1) – 2 = 1 box of oatmeal cookies, for a total of 2 boxes, or 12 cookies. Quantity A is greater, so eliminate choices (B) and (C).
Now plug in 10 boxes of chocolate chip cookies:
Quantity A is now 2(10) + 3 = 23 boxes of oatmeal cookies, for a total of 33 boxes, or 198 cookies, and
Quantity B is now 3(10) – 2 = 28 boxes of oatmeal cookies, for a total of 38 boxes, or 228 cookies.
Quantity B is now greater, so eliminate choice (A), and you’re left with choice (D).
First, plug in 1 for the number of boxes of chocolate chip cookies.
In Quantity A, if Sally buys 1 box of chocolate chip cookies, then she buys 2(1) + 3 = 5 boxes of oatmeal cookies, for a total of 6 boxes, or 36 cookies.
In Quantity B, if Sally buys 1 box of chocolate chip cookies, then she buys 3(1) – 2 = 1 box of oatmeal cookies, for a total of 2 boxes, or 12 cookies. Quantity A is greater, so eliminate choices (B) and (C).
Now plug in 10 boxes of chocolate chip cookies:
Quantity A is now 2(10) + 3 = 23 boxes of oatmeal cookies, for a total of 33 boxes, or 198 cookies, and
Quantity B is now 3(10) – 2 = 28 boxes of oatmeal cookies, for a total of 38 boxes, or 228 cookies.
Quantity B is now greater, so eliminate choice (A), and you’re left with choice (D).
Re: Every box of cookies contains exactly 6 cookies.
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05 Mar 2018, 18:20
05 Mar 2018, 18:20
1
The total number of cookies purchased if Sally purchased 3 more than twice as many boxes of oatmeal cookies as boxes of chocolate chip cookies
oatmeal_cookies = 3 + 2* chocolate_cookies
The total number of cookies purchased if Sally purchased 2 fewer than 3 times as many boxes of oatmeal cookies as boxes of chocolate chip cookies
3*oatmeal_cookies - 2 = chocolate_cookies -> oatmeal_cookies = (chocolate_cookies + 2)/3
and we know that Sally has bought both cookies, their sum is oatmeal + chocolate. Having the relation of these two we calculate their sum in A and B:
A: oatmeal + chocolate = 3 + 2* chocolate_cookies + chocolate_cookies = 3 + 3* chocolate_cookies
B: oatmeal + chocolate = (chocolate_cookies + 2)/3 + chocolate_cookies = 6 + 4/3*chocolate_cookies
comparing A and B we notice for different values of chocolate_cookies A and B are sometimes greater and sometimes less.
3 + 3* chocolate_cookies 6 + 4/3*chocolate_cookies (adding -3)
3* chocolate_cookies 3 + 4/3*chocolate_cookies (deleting 4/3*chocolate)
5/3*chocolate_cookies 3
and these two are not comparable.
if chocolate_cookies is 3 : A > B
if chocolate_cookies is 1 : A < B
oatmeal_cookies = 3 + 2* chocolate_cookies
The total number of cookies purchased if Sally purchased 2 fewer than 3 times as many boxes of oatmeal cookies as boxes of chocolate chip cookies
3*oatmeal_cookies - 2 = chocolate_cookies -> oatmeal_cookies = (chocolate_cookies + 2)/3
and we know that Sally has bought both cookies, their sum is oatmeal + chocolate. Having the relation of these two we calculate their sum in A and B:
A: oatmeal + chocolate = 3 + 2* chocolate_cookies + chocolate_cookies = 3 + 3* chocolate_cookies
B: oatmeal + chocolate = (chocolate_cookies + 2)/3 + chocolate_cookies = 6 + 4/3*chocolate_cookies
comparing A and B we notice for different values of chocolate_cookies A and B are sometimes greater and sometimes less.
3 + 3* chocolate_cookies 6 + 4/3*chocolate_cookies (adding -3)
3* chocolate_cookies 3 + 4/3*chocolate_cookies (deleting 4/3*chocolate)
5/3*chocolate_cookies 3
and these two are not comparable.
if chocolate_cookies is 3 : A > B
if chocolate_cookies is 1 : A < B
