# How much of each chemical is needed to make 750 kg of the plant food, if a plant food is to be made from three chemicals and 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?

Mar 31, 2015

1st chemical 50 kg, 2nd chemical 400 kg, 3rd chemical 300 kg

#### Explanation:

Let $a$, $b$, $c$ be the weights of three chemicals, then as per the question

$a + b + c = 750$ and

a+b= 60% "of 750" = 750*60/100 = 450

Clearly $c$ will be $750 - 450 = \text{300 kg}$

Now ratio of $b$ to $c$ is $4 : 3$, that means

$\frac{b}{c} = \frac{4}{3} \iff 3 b = 4 c$

Since $c$ is $\text{300 kg}$, as calculated above,

$3 b = 3 \left(400\right) = 1200$

Hence $b = 400$. Now, since

$a + b = 450 \implies a = 450 - 400 = \text{50 kg}$

Thus chemicals $a$, $b$, and $c$ in $\text{750 kg}$ of plant food would be $\text{50 kg}$, $\text{400 kg}$, and $\text{300 kg}$.