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22 Jan 2019, 02:19
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C
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In a certain solution, the ratio of water to alcohol is 3:1. If water and alcohol combined make up half of the volume of the solution, what percentage of the solution is water?
A 12.5%
B 25%
C 37.5%
D 50%
E 75%
A 12.5%
B 25%
C 37.5%
D 50%
E 75%
22 Jan 2019, 05:46
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Bunuel
In a certain solution, the ratio of water to alcohol is 3:1. If water and alcohol combined make up half of the volume of the solution, what percentage of the solution is water?
A 12.5%
B 25%
C 37.5%
D 50%
E 75%
A 12.5%
B 25%
C 37.5%
D 50%
E 75%
water : alcohol ; 3:1
let total vol ; 100
half ; 50
3*50 / 4 = 37.5%
IMO C
22 Jan 2019, 15:41
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Bunuel
In a certain solution, the ratio of water to alcohol is 3:1. If water and alcohol combined make up half of the volume of the solution, what percentage of the solution is water?
A 12.5%
B 25%
C 37.5%
D 50%
E 75%
Use totals of ratio parts. We need nothing else.A 12.5%
B 25%
C 37.5%
D 50%
E 75%
We have two "halves" of a solution. One half contains only water and alcohol.
The other half contains some liquid other than water and alcohol (mercury or oil, e.g.)
• The water-and-alcohol portion: from its ratio parts, derive total parts of that portion
W : A : TOTAL parts
\(3 : 1 : 4\)
Total parts = \((3 + 1) = 4\)
(Water is 3 of 4 parts. Alcohol is 1 of 4 parts. The concentration here does not matter.
We need total volume, total parts, of the whole amount of the solution.
We use the water/alcohol ratio to calculate what amount "half" of the solution equals.)
• The entire solution contains how many parts?
The 4 parts of water-and-alcohol make up only half of all the liquid in the solution
If 4 parts =\(\frac{1}{2}\) of total parts in the solution, then
8 parts = total number of parts in the solution
The number of parts of water does not change.
• Water is what percentage of the solution [the solution made up of 8 parts]?
Water = 3 parts of 8 parts
Percentage: \(\frac{Part}{Whole}* 100\)
\(\frac{3}{8} = .375 * 100 = 37.5\)
Answer C
