Roland2rule wrote:The number of singles that a baseball player hit increased 11 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 1 percent. If the total number of singles and doubles that she hit increased 2 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?
(A) 1:3
(B) 9:11
(C) 1:1
(D) 2:1
(E) 11:3
This is a MIXTURE problem.
Percent change for singles = +11%.
Percent change for doubles = -1%.
Revenue change for the MIXTURE of singles and doubles = +2%.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Let S = singles and D = doubles.
Step 1: Plot the 3 percent changes on a number line, with the percent changes for S and D on the ends and the percent change for the mixture in the middle.
S +11%....................+2%....................-1% D
Step 2: Calculate the distances between the percentages.
S +11%.......
9.........+2%........
3.........-1% D
Step 3: Determine the ratio in the mixture.
The ratio of S to D is equal to the RECIPROCAL of the distances in red.
S : D = 3:9 = 1:3.
The correct answer is
A.
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