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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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

Explanation:

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

$a + b + c = 750$ $a+b+c= 750$ and

$a + b = 60 % of 750 = 750 \cdot \frac{60}{100} = 450$ $a+b= 60% "of 750" = 750*60/100 = 450$

Clearly $c$ $c$ will be $750 - 450 = 300 kg$ $750-450 = "300 kg"$

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

$\frac{b}{c} = \frac{4}{3} \Leftrightarrow 3 b = 4 c$ $b/c= 4/3 <=> 3b = 4c$

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

$3 b = 3 (400) = 1200$ $3b= 3(400)= 1200$

Hence $b = 400$ $b =400$ . Now, since

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

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

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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?

1 Answer

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