Algebra. Systems of equations. Word problem. Ratio.?

Question

First time I have come across a ratio in a system of equations word problem. The book doesn't even cover ratios for another 3 chapters! Please explain how I would set this word problem up into a system of 3 equations?


A plant food is to be made from three chemicals. The mix must include 60% of the first and second chemicals. The second and third chemicals must be in a ratio of 4 to 3 by weight. How much of each chemical is needed to make 750 kg of the plant food?

Answer 1

Let the chemicals be A, B, C, and their respective percentages in the plant food be a, b, c.
Then b/c = 4/3.................(1)
a + b = 60..................(2)
a + b + c = 100.................(3)
From (2) and (3), c = 40%
From (1) b = 4c/3 = (53 1/3)%
From (3) a = (6 2/3)%
Trust you can work out these percentages of 750kg.