Answer:
a = 57 kg
b = 453 kg
c = 340 kg
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.
[tex]\frac{b}{c} =\frac{4}{3}[/tex] [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]:
[tex]\frac{b}{c} =\frac{4}{3}\\b = \frac{4}{3} \times 340kg=453kg[/tex]
From [3]:
a + b + c = 850 kg
a = 850 kg - b - c
a = 850 kg - 453 kg - 340 kg = 57 kg
