SOLUTION: 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

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.
RELATED QUESTIONS
Cement, gravel, and sand are to be combined into a mixture in the ratio of 3:5:7... (answered by stanbon,jim_thompson5910)

help Im am completely lost! weights of a certain model of fully loaded gravel trucks... (answered by rothauserc)

You are making 10 tons of concrete that is 62% cement by mixing a 20% cement mixture... (answered by lwsshak3,josmiceli)

You are making 10 tons of concrete that is 51% cement by mixing a 14% cement mixture with (answered by josgarithmetic)

You are making 10 tons of concrete that is 36.2% cement by mixing a 17% cement mix-... (answered by ewatrrr,josmiceli)

You are making 10 tons of concrete that is 61.1% cement by mixing a 19% cement mixture... (answered by ankor@dixie-net.com)

Two gravel trucks have the capacity of 13 tons and 15 tons. They made a total of 18 round (answered by josgarithmetic)

A mixture contains 10 kg of sand, 20kg of cement and 5 kg of gravel. Find the ratio of... (answered by josgarithmetic)

You are making 10 tons of concrete that is 59.3% cement by mixing a 39% cement mix-... (answered by scott8148)