A plant food is to be made from 3 chemicals. The mix must include 60% of the first and second chemicals. The second and third chemicals must be in the ratio of 4:3 by weight. How much of each chemical is needed to make 750kg of the plant food?
The weights of the first, second and third chemicals are 50kg, 300kg, and 400kg respectively.
Let's let the weight of each of the first, second and third chemicals be
We have also been told that the weight of the first and second chemical represents
Finally, we are given the ratio of the second and third chemicals as
which we can solve for
We now have 3 equations and 3 unknowns. Looking at the equations, we notice that the first and second equations differ only by the presence of
if we subtract the second equation from this equation we get:
Now we can substitute the total weight of plant food for
Now we can solve for
Finally, lets use the first equation for the total weight rearranged to solve for
Its always a good idea to check the answers, so lets make sure that we got the percentage of first and second ingredients and ratio of the second and third ingredients correct: