SOLUTION: new brand of plant fertilizer is to be made from three different types of chemicals (A, B, C). The mixture includes 80% of chemicals A and B. Chemical B and C must be in ratio of

Question 859007: new brand of plant fertilizer is to be made from three different types of chemicals (A, B, C).
The mixture includes 80% of chemicals A and B.
Chemical B and C must be in ratio of 3 to 4 by weight.
How much of each type of chemical is needed to make 600kg of plant fertilizer?

Answer by Awesom3guy(31) (Show Source): You can put this solution on YOUR website!
Set up a system of three equations with three unknowns.
new brand of plant fertilizer is to be made from three different types of chemicals (A, B, C).
A + B + C = 600
The mixture includes 80% of chemicals A and B.
A + B = 600*0.8
A + B = 480

Chemical B and C must be in ratio of 3 to 4 by weight.
B = (3/4)C

Now plug in the value of any variable from one equation to the other two, in the place of that variable. Say, from the last equation.
We will plug in (3/4)C in both the top two equations.
A + B + C = 600
A + (3/4)C + C = 600
A + (7/4/)C = 600

A + B = 480
A + (3/4)C = 480

Now we have the two equations with two variables (B was eliminated):
A + (7/4)C = 600
A + (3/4)C = 480

From the first equation:
A = 600 - (7/4)C
Plug this into the second equation:
600 - (7/4)C + (3/4)C = 480
Now we collect like terms and:
-(4/4)C = -120
C = 120

Now we have that it takes 120 kg of chemical C for the mixture.
Next, we solve for A and B.

Now you know C, so from the equation:
B = (3/4)C
B = 3/4 * 120
B = 90

And finally, solve for A.
A + B = 480
A = 480 - B
A = 480 - 90
A = 390

It takes 390 kg of chemical A, 90 kg of B and 120 kg of C.

We also want to check.
They must add to 600.
390 + 90 + 120 = 600
A and B together must make 80% of 600.
(390 + 90)/600 = 0.8
And B must equal 3/4 of C
90 * (3/4) = 120.

Great. Hope that helps:)
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