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

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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)   (Show Source): You can put this solution on YOUR website!
First, second, and third ingredients
x, y, z






-

-


-

The three equations from the description are:


Note that the expression occurs twice in the list of equations.

Subtract the corresponding members to find

















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

------------------------------------
Answer by greenestamps(13200)   (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)   (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)

     = ,    or   3y = 4z.     (3)


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

    z = 700 - 490 = 210 kg.


Then from (3),  y =  = 280.



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

Solved.


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