# 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?

Jul 3, 2018

First chemical $50$ kilograms, second $400$ kilograms and third $300$ kilograms to make$750$ kilograms of plant food.

#### Explanation:

Let the three chemicals be $x , y$ and $z$ kilograms (in order of first, second and third) and we have

$x + y + z = 750$ .................(A)

Further as 60% of $750$ is $750 \times \frac{60}{100} = 450$, we have

$x + y = 450$ and hence $z = 750 - 450 = 300$

As $y$ and $z$ are in ratio $4 : 3$, if we have $300$ kilograms of $z$, we would have $400$ kilograms of $y$

and hence $x = 450 - 400 = 50$ kilograms.