Problem: Two identical jars are filled with alcohol solutions, the ratio of the volume of alcohol to the volume of water being p:1 in one jar and q:1 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
Answer Choices:
A. 2p+q
B. p+qp2+q2
C. p+q2pq
D. 3(p+q)2(p2+pq+q2)
E. p+q+2p+q+2pq
Solution:
If each jar contains a total of x liters of solution, then one jar contains p+1px liters of alcohol and p+1x liters of water, and the other jar contains q+1qx liters of alcohol and q+1x liters of water. The ratio of the volume of alcohol to the volume of water in the mixture is then
(p+11+q+11)x(p+1p+q+1q)x=(q+1)+(p+1)p(q+1)+q(p+1)=p+q+2p+q+2pq