joemama142000 wrote:

The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft

(B) 2.5 ft

(C) 2.8 ft

(D) 3.0 ft

(E) 3.2 ft

OCDianaOC wrote:

Can you show me step-by-step how to solve this one? I'm missing something...

OCDianaOC - This question's wording is not easy. I rephrased it.

Given: a chemical concentration of 6

Given: a formula that will tell how deep the water is at a particular concentration, IF we have the concentration (we do)

Formula: \(3 + \frac{4}{\sqrt{5-x}}\)

Set the formula equal to concentration. The concentration of 6, in tandem with the formula, will yield depth.

\(3 + \frac{4}{\sqrt{5-x}} =

6\)

Subtract 3 from both sides:

\(\frac{4}{\sqrt{5-x}} = 3\)

Square both sides:

\((\frac{4^2}{(\sqrt{5-x})^2}) = 3^2\)

\((\frac{16}{(5-x)}) = 9\)

Multiply both sides by denominator and solve:

\(16 = 9(5 - x)\)

\(16 = 45 - 9x\)

\(9x = 29\)

\(x = \frac{29}{9} = 3.2\) feet

Answer E

Hope that helps.

**The language "where 0 < x < 4," is mostly irrelevant. It's to keep the denominator in the formula positive. (Can't divide by zero, can't take the square root of a negative number.)