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D
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Difficulty:
95%
(hard)
Question Stats:
34% (02:31) correct
66%
(03:33)
wrong
based on 32
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Tomasa is making sangria for a party. She pours into a vat 40 ounces of wine that is 13% alcohol by volume and 24 ounces of rum that is 35% alcohol by volume. At least how many entire 16-ounce bottles of alcohol-free soda must she add to the vat so that the resulting sangria is less than 5% alcohol?
A) 11
B) 12
C) 13
D) 14
E) 15
A) 11
B) 12
C) 13
D) 14
E) 15
22 Apr 2026, 01:01
Kudos
Bookmarks
there are two mixtures here. 1st that is formed by wine and rum containing some alcohol %age and 2nd mixting soda(0 alcohol) with mixture obtained from 1st calc.
1st mixture.
13%----x-------35%
(35-x)/(x-13) = 40/24 ( ratio of their presence in the newly formed mixture = ratio of actual weights of wine and rum )
x= 21.5
now next mixture
0%-----5%-------21.5%
SODA MIX
Presence of soda weight of soda Y
------------------ = ----------------- = ------------
mix weight of mix 64
16.5/5 = Y/64
Y= 33*64
now to get the number of bottles we must divide Y with 16
i.e, Y/16 = 13.2
So we need atleast 13.2 or more bottles of soda to ensure that alcohol is less than 5%
Hence Answer D.
1st mixture.
13%----x-------35%
(35-x)/(x-13) = 40/24 ( ratio of their presence in the newly formed mixture = ratio of actual weights of wine and rum )
x= 21.5
now next mixture
0%-----5%-------21.5%
SODA MIX
Presence of soda weight of soda Y
------------------ = ----------------- = ------------
mix weight of mix 64
16.5/5 = Y/64
Y= 33*64
now to get the number of bottles we must divide Y with 16
i.e, Y/16 = 13.2
So we need atleast 13.2 or more bottles of soda to ensure that alcohol is less than 5%
Hence Answer D.
kevincan
22 Apr 2026, 01:51
Kudos
Bookmarks
24% alcohol in 40 = 5.2.
35% alcohol in 24 = 8.4.
Our net result:
5.2+8.4/(64+x) < 1/20
x>208.
No.of 16 ounce bottles asked, thus
208/16 = 13.
But we need x>13. So 14 is the least number of such bottles.
Answer: Option D
35% alcohol in 24 = 8.4.
Our net result:
5.2+8.4/(64+x) < 1/20
x>208.
No.of 16 ounce bottles asked, thus
208/16 = 13.
But we need x>13. So 14 is the least number of such bottles.
Answer: Option D
kevincan
