Question

How many liters of a 35% acid solution and a 85% acid solution must be used to produce 80 liters of a 40% acid solution? I already know the answer but I don't understand the steps to find it such as getting the equations.

Answer 1

72 liters of 35% acid solution and 8 liters of 85% acid solution

Explanation:

This is a very simple mixture problem.

We let the number of liters of 35% acid solution be "x"

and

let the number of liters of 85% acid solution be "y"

Now,

we can say:

0.35x + 0.85y = 0.4(80) [we have followed "Percentage*amount" ]

Also, we know two solution amount would be 80 liters, thus we can say:

x + y = 80

or x = 80 - y

Now we substitute this into 1st equation and solve for y first. Shown below:

`0.35x + 0.85y = 0.4(80)\\0.35x + 0.85y = 32\\0.35(80-y)+0.85y=32\\28-0.35y+0.85y=32\\0.5y=4\\y=8`

Thus, x = 80 - 8 = 72

So we use 72 liters of 35% acid solution and 8 liters of 85% acid solution