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?

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Answer 1 · 2018-07-03T05:20:46

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

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

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

Further as $60 %$ $60%$ of $750$ $750$ is $750 \times \frac{60}{100} = 450$ $750xx60/100=450$ , we have

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

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

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