Chapter 4.1, Problem 46PPS

a.

To determine

To Find: The number of weeks need to collect the money to buy the TV.

Answer to Problem 46PPS

The number of weeks is 16.

Explanation of Solution

Given Information:

The price of TV $\mathrm{C}=\mathrm{\$}936$

The money Ricky has ${\mathrm{P}}_{\mathrm{i}}=\mathrm{\$}40$

The cost for gas for three lawns ${\mathrm{C}}_{\text{gas}}=\mathrm{\$}6$

The charges for mowing the lawn ${\mathrm{P}}_{\text{gas}}=\mathrm{\$}20$

Calculation:

Write the expression for the number of weeks needed to buy the TV.

  $\begin{array}{c}{\mathrm{P}}_{\mathrm{i}}+\left(3{\mathrm{P}}_{\text{mowing}}-{\mathrm{c}}_{\text{gas}}\right)\mathrm{n}+\left({\mathrm{P}}_{\text{route}}\right)\times \frac{\mathrm{n}}{4}=\mathrm{C}\\ \left(3{\mathrm{P}}_{\text{mowing}}-{\mathrm{c}}_{\text{gas}}\right)\mathrm{n}+\left({\mathrm{P}}_{\text{route}}\right)\times \frac{\mathrm{n}}{4}=\mathrm{C}-{\mathrm{P}}_{\mathrm{i}}\\ \mathrm{n}=\frac{\mathrm{C}-{\mathrm{P}}_{\mathrm{i}}}{\left(3{\mathrm{P}}_{\text{mowing}}-{\mathrm{c}}_{\text{gas}}\right)+\frac{\left({\mathrm{P}}_{\text{route}}\right)}{4}}\end{array}$

Substitute the values in the above expression.

  $\begin{array}{c}\mathrm{n}=\frac{936-40}{\left(3\times 20-6\right)+\frac{\left(45\right)}{4}}\\ =13.731\end{array}$

As the person needs to work for complete month to get paid for it so round off the number of week in terms of completion of months.

Thus, the number of weeks is 16.

b.

To determine

To Explain: The process for the solution.

Answer to Problem 46PPS

The steps should be as follows:

1. The amount earned from the mowing the lawns is $\mathrm{\$}864$ .
2. The amount earned from the paper routing is $\mathrm{\$}180$ .

Explanation of Solution

Given Information:

The number of weeks worked is 16.

Calculation:

1. Write the amount earned by mowing the lawns.

  $$

  $\begin{array}{c}{\mathrm{C}}_{\text{mowing}}=\left(3{\mathrm{P}}_{\text{mowing}}-{\mathrm{c}}_{\text{gas}}\right)\mathrm{n}\\ =\left(3{\mathrm{P}}_{\text{mowing}}-{\mathrm{c}}_{\text{gas}}\right)\mathrm{n}\\ =\left(3\times 20-6\right)\times 16\\ =\mathrm{\$}864\end{array}$

2. Calculate the amount earned by the paper routing.

  $\begin{array}{c}{\mathrm{C}}_{\text{Routing}}=\left(45\right)\frac{\mathrm{n}}{4}\\ =\left(45\right)\frac{16}{4}\\ =45\times 4\\ =\mathrm{\$}180\end{array}$

c.

To determine

To find: The assumptions about the process.

Answer to Problem 46PPS

The assumptions are follows:

1. The payments can be given on the completion of the period such as week or month.
2. Each month considered to have 4 weeks in it. As it is not possible to find the exact no. of weeks in each month. Thus 4 weeks are counted in each month

Explanation of Solution

Given Information:

The price of TV $\mathrm{C}=\mathrm{\$}936$

The money Ricky has ${\mathrm{P}}_{\mathrm{i}}=\mathrm{\$}40$

The cost for gas for three lawns ${\mathrm{C}}_{\text{gas}}=\mathrm{\$}6$

The charges for mowing the lawn ${\mathrm{P}}_{\text{gas}}=\mathrm{\$}20$

Calculation:

The assumptions for the process are:

1. The payments can be given on the completion of the period such as week or month.
2. Each month considered to have 4 weeks in it. As it is not possible to find the exact no. of weeks in each month. Thus 4 weeks are counted in each month.