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# GMAT: Math 52

240-244, pgs. 185-186. Created by Sal Khan.

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• What are the steps in solving math problems like this 3-(-52) • Mixture X+Y contains some bluegrass in it, which originates from X, therefore the % of mixture X in X+Y is the %ryegrass from X + the% bluegrass from X / everything.

Why are we ignoring the fact X+Y contains some bluegrass from X. We are in fact answering percent of the ryegrass in X /ryegrass in mixture.

I have no issues with algebra, it´s the wording which I feel is incorrect • Try to forget what is ryegrass, bluegrass and fescue. Those specifications are just trying to confuse you. What's more helpful is if you try to reduce the number of variables.

Here's an alternative way to think about it.
40% of X is rye (R) and 60% of X is other (O).
25% of Y is rye (R) and 75% of Y is other (O).
When you mix X and Y, you get 30% R + 70% O.

Multiply all percents by 100 to get numbers that are more manageable. This info helps you set up the following system of equations:

40X + 25Y = 30
60X + 75Y = 70

Now solve for X by eliminating Y. To do so, find the Greatest Common Factor (GCF) for 25 and 75. In this case, GCF = 75, so all you need to do is multiply the first equation by -3 so you can cancel out the Y.

-120X - 75Y = -90
60X + 75Y = 70

Y cancels out and you are left with:

-60X = -20
X = 1/3 = 33 1/3%