SOLUTION: A plant food is to be made from three chemicals. The combined amounts of the first two chemicals must be 70​% of the resulting mix. The second and third chemicals must be in

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A plant food is to be made from three chemicals. The combined amounts of the first two chemicals must be 70​% of the resulting mix. The second and third chemicals must be in      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1115859: A plant food is to be made from three chemicals. The combined amounts of the first two chemicals must be 70​% of the resulting mix. The second and third chemicals must be in the ratio of 4 to 3 by weight. How much of each chemical is needed to make 700 kg of the plant​ food?
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
First, second, and third ingredients
x, y, z

%28x%2By%29%2F700=0.7
x%2By=700%2A0.7
x%2By=7%2A7%2A100%2A0.1
x%2By=49%2A10
x%2By=490
-
y%2Fz=4%2F3
-
x%2By%2Bz=700

-

The three equations from the description are:
system%28x%2By%2Bz=700%2Cx%2By=490%2C3y=4z%29

Note that the expression x%2By occurs twice in the list of equations.
system%28%28x%2By%29%2Bz=700%2Cx%2By=490%29
Subtract the corresponding members to find z=700-490
highlight%28z=210%29

3y=4z
y=4z%2F3
y=4%2A210%2F3
y=4%2A70
highlight%28y=280%29


x%2By=490
x=490-y
x=490-280
highlight%28x=210%29




-----------------------------------
    MATERIAL           KILOGRAMS
x   first chemical      210
y   second chemical     280
z   third chemical      210

------------------------------------

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The combined weight of the first two is 70% of the total weight, so the weight of the third chemical is 30% of the total.

If the ratio of the second and third chemicals is 4:3 and the third chemical is 30% of the total weight, then the second chemical is 40% of the total weight.

If the second chemical is 40% of the total weight and the third is 30% of the total, then the first is 30% of the total.

So 30% first chemical, 40% second, and 30% third. With a total weight of 700 kg, you need
210 kg of first
280 kg is second
210 kg of third

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x = 1st chemical amount (in kilograms);

    y = 2nd chemical amount;

    z = 3rd chemical amount.


From the condition, we have


x + y + z = 700                  (1)

x + y     = 490                  (2)    (70% of 700 kg)

    y%2Fz = 4%2F3,    or   3y = 4z.     (3)


Subtract eq(2) from eq(1). You will get

    z = 700 - 490 = 210 kg.


Then from (3),  y = %284%2A210%29%2F3 = 280.



Then from (1),  x = 700 - 280 - 210 = 210.

Solved.