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Cindy bought 48 containers of soda, all either 12-ounce cans
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14 Jun 2018, 14:12
14 Jun 2018, 14:12
Expert Reply
00:00
Question Stats:
78% (01:54) correct
21% (02:12) wrong based on 46 sessions
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Cindy bought 48 containers of soda, all either 12-ounce cans or 20-ounce bottles. If the number of ounces she purchased in cans was equal to the number of ounces she purchased in bottles, how many bottles of soda did Cindy buy?
(A) 18
(B) 21
(C) 24
(D) 27
(E) 30
(A) 18
(B) 21
(C) 24
(D) 27
(E) 30
Re: Cindy bought 48 containers of soda, all either 12-ounce cans
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16 Jun 2018, 13:50
16 Jun 2018, 13:50
We are given two equations in the question.
Cindy bought 48 containers of soda, all either 12-ounce cans or 20-ounce bottles.
\((C+B)=48\)
the number of ounces she purchased in cans was equal to the number of ounces she purchased in bottles
\(12(c)=20(b)\)
Since we want to know how many bottles are needed, we can manipulate the first equation and then plug it into the second.
\(C=48-b\)
\(12(48-b)=20(b)\)
\(576-12b=20b\)
\(576=32b\)
\(18=b\)
The answer is A.
Cindy bought 48 containers of soda, all either 12-ounce cans or 20-ounce bottles.
\((C+B)=48\)
the number of ounces she purchased in cans was equal to the number of ounces she purchased in bottles
\(12(c)=20(b)\)
Since we want to know how many bottles are needed, we can manipulate the first equation and then plug it into the second.
\(C=48-b\)
\(12(48-b)=20(b)\)
\(576-12b=20b\)
\(576=32b\)
\(18=b\)
The answer is A.
Re: Cindy bought 48 containers of soda, all either 12-ounce cans
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05 Jul 2018, 01:46
05 Jul 2018, 01:46
Expert Reply
Explanation
Define variables and translate equations from the given information:
Number of bottles = b
Number of cans = c
\(b + c = 48\) (Number of containers purchased)
\(12c = 20b\) (Equal number of ounces in bottles purchased and cans purchased)
The question asks for b, so isolate c in the first equation and substitute into the second equation:
\(c = 48 - b\)
\(12(48 - b) = 20b\)
\(576 - 12b = 20b\)
\(576 = 32b\)
\(b = 18\)
Check the answer. If Cindy bought 18 bottles, she bought 30 cans. The number of ounces in the bottles was 18 × 20 = 360. The number of ounces in the cans was 30 × 12 = 360.
Hence option A is correct!
Define variables and translate equations from the given information:
Number of bottles = b
Number of cans = c
\(b + c = 48\) (Number of containers purchased)
\(12c = 20b\) (Equal number of ounces in bottles purchased and cans purchased)
The question asks for b, so isolate c in the first equation and substitute into the second equation:
\(c = 48 - b\)
\(12(48 - b) = 20b\)
\(576 - 12b = 20b\)
\(576 = 32b\)
\(b = 18\)
Check the answer. If Cindy bought 18 bottles, she bought 30 cans. The number of ounces in the bottles was 18 × 20 = 360. The number of ounces in the cans was 30 × 12 = 360.
Hence option A is correct!
