Question

A scientist needs 10 liters of a 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. To the nearest tenth of a liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs? Write and solve an equation to match the situation. Equation: [ Select ] Solution: [ Select ] liters of 5% [ Select ] liters of 40%

Answer 1

We can write an equation for this problem.

10 * 0.20 = 0.05x + 0.40(10 - x)

~Simplify

2 = 0.05x + 4 - 0.40x

~Combine like terms

2 = 4 - 0.35x

~Subtract 4 to both sides

-2 = 0.35x

~Divide 0.35 to both sides

40/7 = x

~Subtract by 10

10 - 40/7 = 30/7

30/7 of 40%

Best of Luck!

Answer 2

5 5/7 liters of 5%

4 2/7 of the 40 %

Explanation:

we need 10 liter of a 20 % solution

We have x liters of 5% and since there is a total of 10 liters we have 10-x of the 40 % solutions

10 * .20 = .05 x + .40 ( 10-x)

2 = .05x +4 - .4x

Combine like terms

2 = 4- .35x

Subtract 4 from each side

2-4 = -.35x

-2 = -.35x

Divide by -.35

-2/.-35 =x

40/7 =x

5 5/7 =x

10 -5 5/7 = 4 2/7

4 2/7 of the 40 %