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
Mixtures
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Using the "tug of war" method, we can figure out the ratio of X to Y from the stem alone:
Y X
2--5----10
5-2 = 3
10-5 = 5
X:Y = 3:5
Now we just need something that will allow us to go from a proportion to an exact value.
1) Perfect! Using the ratio above, we can determine that x is 6.
2) This works as well. From the stem, we can set up the equation .1x + .02y = .05(z), and S2 gives us the equation x + y = 16. We can solve two independent linear equations.
D
Y X
2--5----10
5-2 = 3
10-5 = 5
X:Y = 3:5
Now we just need something that will allow us to go from a proportion to an exact value.
1) Perfect! Using the ratio above, we can determine that x is 6.
2) This works as well. From the stem, we can set up the equation .1x + .02y = .05(z), and S2 gives us the equation x + y = 16. We can solve two independent linear equations.
D
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