Question

Scientist needs 10 liters of a 20% acid solution for an experiment, but she has

nly a 5% solution and a 40% solution. To the nearest tenth of a ter about
ow many liters of the 5% and the 40% solutions should she mix to get the
plution she needs? Write and solve an equation to match the situation

Answer 1

40/7 liters of 5% acid, 30/7 liters of 40% acid

Explanation:

We need to find a value so that the amount of acid is 20% = 1/5 of the total amount of liquid. Therefore, if x represents the total amount of liquid, we can say that

1/5 (x) = amount of acid at the end

We know that we need 10 liters of solution, so

1/5 (10) = amount of acid at the end = 2 liters

If we have y amount of 5% = 0.05 acid solution and z amount of 40% =0.4 acid solution, the total amount of acid will be equal to

0.05 * y (amount of acid from 0.05 acid solution) + 0.4 * z = 2

Next, we know that the total amount of liters is 10, and the liters come from the 5% and 40% acid solutions, so

y + z = 10

We therefore have

0.05 * y + 0.4 * z = 2

y + z = 10

One way to solve this is to solve for z in the second equation and plug that into the first.

subtract y from both sides in the second equation to isolate z

10 -y = z

plug 10-y in for z in the second equation

0.05 * y + 0.4 * (10-y) = 2

0.05 * y + 4 -0.4 * y = 2

-0.35 * y + 4 = 2

subtract 4 from both sides to isolate the y and its coefficient

-0.35y = -2

divide both sides by -0.35 to isolate y

y = -2/-0.35 = 40/7 * (-0.05/-0.05) = 40/7 liters

z = 10 - y = 10-40/7 = 70/7 - 40/7 = 30/7 liters