Chapter 4.1, Problem 42PPS

To determine

To find the equation that represents the given situation.

Answer to Problem 42PPS

  $y=-\frac{1}{3}x+72$ & option A is correct.

Explanation of Solution

Given:

The current water level of a swimming pool is 6 feet. The rate of evaporation is $\frac{1}{3}$ inch per day.

Calculation:

Total water in the swimming pool is,

  $\begin{array}{l}6\text{feet}=6\times 12\text{inches}\left[\because 1\text{feet}=12\text{inches}\right]\\ =72\text{inches}\end{array}$

Now let x be the number of days of evaporation & y be the water level of the swimming pool.

Then water evaporated in x days is $\frac{1}{3}x$ .

Therefore total water level after x days is,

  $\begin{array}{l}y=\text{Total}\text{water}-\text{water}\text{evaporated}\text{in}x\text{days}\\ \Rightarrow y=72-\frac{1}{3}x\\ \Rightarrow y=-\frac{1}{3}x+72\end{array}$

Hence option A is correct.