Question

A plant food is to be made from three chemicals. The combined amounts of the first two chemicals must be 60​% 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 850 kg of the plant​ food?

Answer 1

a = 57 kg

b = 453 kg

c = 340 kg

Step-by-step explanation:

Let's call the amount of each chemical a, b and c. We can write the statements in a symbolic way.

The combined amounts of the first two chemicals must be 60​% of the resulting mix.

a + b = 0.6 × 850 kg

a + b = 510 kg [1]

The second and third chemicals must be in the ratio of 4 to 3 by weight.

`(b)/(c) =(4)/(3)` [2]

The total amount is 850 kg.

a + b + c = 850 kg [3]

From [3], we have,

a + b + c = 850 kg

a + b = 850 kg - c [4]

Now, we can equal [1] and [4].

510 kg = 850 kg - c

c = 340 kg

If we replace this value in [2]:

`(b)/(c) =(4)/(3)\\b = (4)/(3) * 340kg=453kg`

From [3]:

a + b + c = 850 kg

a = 850 kg - b - c

a = 850 kg - 453 kg - 340 kg = 57 kg