Chapter 6.1, Problem 38E

To determine

To calculate: Whether there is enough money to buy the guitar.

Answer to Problem 38E

The money earned is $\$405$ . Since cost of guitar is $\$400$ , there is enough money to buy the guitar.

Explanation of Solution

Given information:

The cost of guitar = $\$400$

Money earned per hour = $\$9$

No. of work hours each week = $15$

No of weeks= $3$

Calculation:

To calculate whether there is enough money to buy the guitar, find the money earned. To find the money earned, first calculate the total number of work hours and then find the money earned for that number of hours.

Since work hours per week is $15$ , it can be written as:

  $\frac{15\text{ h}}{1\text{ week}}$

To find the number of work hours in $3$ weeks, multiply numerator and denominator by $3$$\begin{array}{l}\frac{15\text{ h}\times \text{3}}{1\text{ week}\times \text{3}}\\ \Rightarrow \frac{45\text{ h}}{3\text{ weeks}}\end{array}$

Therefore, the number of work hours for $3$ weeks is $45$ .

Since the money earned per hour is $\$9$ , it can be written as:

  $\frac{\$9}{1\text{ hour}}$

To find money earned in $45$ hours, multiply numerator and denominator by $45$

  $\begin{array}{l}\frac{\$9\times 45}{1\text{ hour}\times \text{45}}\\ \Rightarrow \frac{\$405}{45\text{ h}}\end{array}$

Therefore, the money earned in $45$ hours is $\$405$ .

Since cost of guitar is $\$400$ and money earned is $\$405$ , there is enough money to buy the guitar.