Question

The concentration of a saline solution is given by the function 1%2Bx%7D" id="TexFormula1" title="C(x)=\frac{0.2}{1+x}" alt="C(x)=\frac{0.2}{1+x}" align="absmiddle" class="latex-formula">, 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

Answer:

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

Step-by-step explanation:

The concentration of a saline solution is given by

                        C(x) = $\frac{0.2}{1+x}$

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 = $\frac{0.2}{1+x}$

Rearranging,

1 + x = $\frac{0.2}{0.07}$

1 + x = 2.86

x = 1.86 L

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