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?

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Answer 1 · 2015-03-31T03:46:51

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

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 $750-450 = "300 kg"$

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

$b/c= 4/3 <=> 3b = 4c$

Since $c$ is $"300 kg"$ , as calculated above,

$3b= 3(400)= 1200$

Hence $b =400$ . Now, since

$a+b =450 implies a= 450-400 = "50 kg"$

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