SOLUTION: How much clay do you need to add to 8m^3 of soil with 30% clay in order to make a soil with 60%?

Question 1015703: How much clay do you need to add to 8m^3 of soil with 30% clay in order to make a soil with 60%?
Found 2 solutions by fractalier, LinnW:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the amount you are adding, x. Then we write
8(.30) + x(1.00) = (8+x)(.60)
2.4 + x = 4.8 + .6x
.4x = 2.4
x = 6 m^3 of pure clay
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Let x = the amount of clay to add
of soil at 30% = of clay
x of soil at 100% = x of clay
( x + 8 ) at 60% = 0.60(x+8)
2.4 + x = 0.60(x+8)
That is the amount of clay in the original mixture plus
the amount of clay in x must give us a mixture of the total
amount of material,(x+8) that is in our final mixture.
The first step is to add -2.4 to each side
x = 0.60(x+8) -2.4
x = 0.6x + 4.8 -2.4
x = 0.6x + 2.4
add -0.6x to each side
0.4x = 2.4
divide each side by 0.4
x = 6
Let's verify that this is correct.
Our original amount of material is of material.
The amount of this material that is clay is 2.4 + 6
The percentage of our new material that is clay
is (2.4 + 6)/14 = 60 %
So 6 m^3 of clay is what we want.
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