Chapter SH, Problem 8.5MPS

(a)

To determine

To calculate: To write a direct variation equation relating the population $p$ and the amount of water used $w$

Answer to Problem 8.5MPS

The equation relating the population $p$ and the amount of water used $w$ is $w=\frac{40}{3}p$

Explanation of Solution

Given information: The amount of water used in a community varies directly with the population. About $18$ million people living in Florida use $2.4$ trillion gallons of water a year

Calculation:

Let the population be $p$

Let the amount of water be $w$

Given that about $18$ million people living in Florida use $2.4$ trillion gallons of water a year

Therefore,

  $18$ million of population used $=2.4\times 100million$

1 people used $=\frac{2.4\times 100million}{18million}$

Thus, equation relating the population $p$ and the amount of water used $w$ is given as

  $\begin{array}{l}w=\frac{2.4\times 100million}{18million}\times p\\ w=\frac{24\times 100}{18\times 10}\times p\\ w=\frac{4\times 10}{3\times 1}\times p\\ w=\frac{40}{3}p\end{array}$

Conclusion:

Hence, equation relating the population $p$ and the amount of water used $w$ is $w=\frac{40}{3}p$

(b)

To determine

To calculate: To estimate the amount of water that will be needed for $24$ million people

Answer to Problem 8.5MPS

The amount of water needed is $320million$

Explanation of Solution

Given information: The amount of water used in a community varies directly with the population. About $18$ million people living in Florida use $2.4$ trillion gallons of water a year

Calculation:

Equation relating the population $p$ and the amount of water used $w$ is given as

  $w=\frac{40}{3}p$

Substituting the values,

  $\begin{array}{l}w=\frac{40}{3}\times 24million\\ w=40\times 8million\\ w=320million\end{array}$

Conclusion:

Hence, the amount of water needed is $320million$