A certain brand of potting soil contains 10% peat and another brand contains 30% peat. How much of each soil should be mixed in order to produce 2 cubic ft of potting soil that is 25% peat?

Question

How would you go about answering the question

Answer 1

Let x be the amount of the first brand of peat and y the amount of the second brand of peat.

In the brand 1 there is x/10 of peat and in brand 2 3y/10 or 0.1x and 0.3y

In the mixture there is 2/4=1/2cu ft of peat, so 0.1x+0.3y=0.5. The amounts of the brands must come to 2cu ft so x+y=2.

That means y=2-x, which we can substitute into the other equation:

0.1x+0.3(2-x)=0.5, 0.1x+0.6-0.3x=0.5, 0.1=0.2x so x=0.1/0.2=0.5cu ft.

So y=2-x=1.5cu ft.

Let’s check if that’s right: amount of brand1 peat=0.5/10=0.05cu ft.

Amount of brand 2 peat=0.3*1.5=0.45cu ft.

Total amount of peat in the mixture is 0.45+0.05=0.5cu ft. And 0.5cu ft in 2cu ft of mixture is 1/4 or 25%.