A contractor combined x tons of a gravel mixture that contained 10% gravel G, by weight, with y tons of a mixture that contained 2 percent of the gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x?
1) y = 10
2) z = 16
x = 10% gravel
y = 2% gravel.
z = the MIXTURE of x and y = 5% gravel.
To determine the required ratio of x to y, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the percentages for x and y on the ends and the percentage for mixture z in the middle.
x 10%-----------5%-----------2% y
Step 2: Calculate the distances between the percentages.
x 10%-----
5-----5%----
3-----2% y
Step 3: Determine the ratio in the mixture.
The required ratio of x to y is equal to the RECIPROCAL of the distances in red.
x:y = 3:5.
Since x:y = 3:5, and 3+5 = 8, every 8 tons of mixture z is composed of 3 tons of x and 5 tons of y.
Statement 1: y=10
Since x:y = 3:5 = 6:10, x=6.
SUFFICIENT.
Statement 2: z=16
Since x:y = 3:5 = 6:10, and 6+10 = 16, the 16 tons of mixture z must be composed of 6 tons of x and 10 tons of y.
SUFFICIENT.
The correct answer is
D.
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