Difference between revisions of "1979 AHSME Problems/Problem 15"
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− | The amount of alcohol in the jars are <math>\frac{p}{p+1}</math> and <math>\frac{q}{q+1}</math>, and the amount of water in the jars are <math>\frac{1}{p+1}</math> and <math>\frac{1}{q+1}</math>. Then the total amount of alcohol is <math>\frac{p}{p+1} + \frac{q}{q+1} = \frac{p+q+2pq}{(p+1)(q+1)}</math>, and the total amount of water is <math>\frac{1}{p+1} and \frac{1}{q+1} = \frac{p+q+2}{(p+1)(q+1)}</math>. The ratio of the volume of alcohol to the volume of water in the mixture is <math>\frac{\frac{p+q+2pq}{(p+1)(q+1}}{\frac{p+q+2}{(p+1)(q+1)}} = \boxed{\textbf{(E) } \frac{p+q+2pq}{p+q+2}}</math>. | + | The amount of alcohol in the jars are <math>\frac{p}{p+1}</math> and <math>\frac{q}{q+1}</math>, and the amount of water in the jars are <math>\frac{1}{p+1}</math> and <math>\frac{1}{q+1}</math>. Then the total amount of alcohol is <math>\frac{p}{p+1} + \frac{q}{q+1} = \frac{p+q+2pq}{(p+1)(q+1)}</math>, and the total amount of water is <math>\frac{1}{p+1} and \frac{1}{q+1} = \frac{p+q+2}{(p+1)(q+1)}</math>. The ratio of the volume of alcohol to the volume of water in the mixture is <math>\frac{\frac{p+q+2pq}{(p+1)(q+1)}}{\frac{p+q+2}{(p+1)(q+1)}} = \boxed{\textbf{(E) } \frac{p+q+2pq}{p+q+2}}</math>. |
== See also == | == See also == |
Latest revision as of 13:21, 6 January 2017
Problem 15
Two identical jars are filled with alcohol solutions, the ratio of the volume of alcohol to the volume of water being
in one jar and
in the other jar. If the entire contents of the two jars are mixed together,
the ratio of the volume of alcohol to the volume of water in the mixture is
Solution
Solution by e_power_pi_times_i
The amount of alcohol in the jars are and
, and the amount of water in the jars are
and
. Then the total amount of alcohol is
, and the total amount of water is
. The ratio of the volume of alcohol to the volume of water in the mixture is
.
See also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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