Question 824856: A contractor combined x tons of a gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture
that contained 2 percent 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
if (1) alone is sufficient to answer the question, answer is A. if (2) alone is sufficient to answer the question, answe is B. if (1) and (2) together are sufficient to answer, then answe is C. if each of (1) and (2) alone is sufficient to answer, answer is D.
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! Two-Part Mixture problem. Let us see what we can do.
Assigning Variables,
L = 2% G
T = 5% G
H = 10% G
z = Amount of mixture in tons
x = amount of the H material
y = amount of the L material
You have six variables, and THREE of them are UNKNOWN. If you wish to solve the problem specifically, you would need to be able to find THREE equations! Right now, x, y, and z are unknown.
You are only able to obtain these equations:
 and 
You are then GIVEN a value for y and if y=10, then you CAN FIND x and z.
You are later given a value for z and if z=16, then you can find values for y and x.
If you are given BOTH x and y, then you only need the simple equation x+y=z to get a value for x.
For just (1) alone, then the unknowns are x and z.
 . Substitute.
 .
Reuse the simple equation ;
 , again, keeping in mind right now x is the solved variable and y is a known variable.
Solve similarly for z.
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