Question

How many liters each of a 10 % acid solution and a 35 % acid solution must be used to produce 40 liters of a 30 % acid solution? (Round to two decimal places if necessary )

Answer 1

To make 40 liters of a 30% acid solution, 8 liters of a 10% acid solution and 32 liters of a 35% acid solution are required. This is determined by setting up and solving a system of equations based on the total volume and acid content.

Step-by-step explanation:

To find out how many liters each of a 10% acid solution and a 35% acid solution are needed to make 40 liters of a 30% acid solution, we can use a system of equations.

Let x be the liters of the 10% solution and y be the liters of the 35% solution. We have two equations:

1. x + y = 40 (total volume)
2. 0.10x + 0.35y = 0.30(40) (acid content)

Solving the system of equations, we can substitute y = 40 - x into the second equation and solve for x:

0.10x + 0.35(40 - x) = 12
0.10x + 14 - 0.35x = 12
-0.25x = -2
x = 8 liters

Therefore, y = 40 - x = 40 - 8 = 32 liters.

We conclude that we need 8 liters of the 10% solution and 32 liters of the 35% solution to obtain 40 liters of a 30% acid solution.

Answer 2

8litres of a 10 % acid solution must be used

32litres of a 35 % acid solution must be used

Explanations:

Let the liters each of a 10 % acid solution be given as "x"

A 35 % acid solution = 40 - x

The weighted combination for x and 40-x is given as:

`0.1x+0.35(40-x)=0.30(40)`

Solve the expression for x:

`\begin{gathered} 0.1x+0.35(40-x)=0.30(40) \\ 0.1x+14-0.35x=12 \\ -0.25x+14=12 \\ -0.25x=12-14 \\ -0.25x=-2 \\ x=(2)/(0.25) \\ x=8 \end{gathered}`

This shows that 8litres of a 10 % acid solution must be used

For the 35% solution, the amount of litres used is:

40 - x = 40 - 8 = 32litres

Hence 32 liters of a 35 % acid solution must be used.