The concentration of a saline solution is given by the function C(x)=(0.2)/(1+x), where x represents the amount of water (in liters) used to dilute the solution. How much water …

Question

The concentration of a saline solution is given by the function
`C(x)=(0.2)/(1+x)`, where x represents the amount of water (in liters) used to dilute the solution. How much water must be added to obtain a solution that is exactly 7% salt?

a. 0.9 L
b. 0.97 L
c. 1 L
d. 1.86 L

Answer 1

We have to add 1.86 L of water to make the solution 7% saline.

Explanation:

The concentration of a saline solution is given by

C(x) =
`(0.2)/(1+x)`

where x represents the amount of water used to dilute the solution.

We have to find how much water must be added to obtain a solution that is 7% saline.

If we see the equation we notice that as we add the value of x, the concentration of the solution decreases.

Here C(x) = 0.07

0.07 =
`(0.2)/(1+x)`

Rearranging,

1 + x =
`(0.2)/(0.07)`

1 + x = 2.86

x = 1.86 L

We have to add 1.86 L of water to make the solution 7% saline.