Chapter 12, Problem 17STP

a.

To determine

To find: Expression for Amanda’s total weekly earnings.

Answer to Problem 17STP

Total weekly earnings $=\left(0+6+4+0+2+6+8\right)\times 6$

Explanation of Solution

Given information:

Amanda earns $\$6$ per hour.

Amanda’s hours at her summer job for one week are listed in the table.

Given

Amanda earns $\$6$ per hour.

Amanda’s hours at her summer job for one week are listed in the table.

Number of hours she works on Sunday $=0$

Number of hours she works on Monday $=6$

Number of hours she works on Tuesday $=4$

Number of hours she works on Wednesday $=0$

Number of hours she works on Thursday $=2$

Number of hours she works on Friday $=6$

Number of hours she works on Saturday $=8$

For each Hour she earns $\$6$

Therefore,

Total weekly earnings $=\left(0+6+4+0+2+6+8\right)\times 6$

Therefore,

Expression for Total weekly earnings

Total weekly earnings $=\left(0+6+4+0+2+6+8\right)\times 6$

b.

To determine

To find: Evaluate the expression from part a by using Distributive Property.

Answer to Problem 17STP

Total Weekly earnings of Amada $=\$156$

Explanation of Solution

Given information:

Amanda earns $\$6$ per hour.

Amanda’s hours at her summer job for one week are listed in the table.

We got

Total weekly earnings $=\left(0+6+4+0+2+6+8\right)\times 6$

On simplifying using Distributive property

We get

  $\Rightarrow$ Total weekly earnings $=\left(0\times 6\right)+\left(6\times 6\right)+\left(4\times 6\right)+\left(0\times 6\right)+\left(2\times 6\right)+\left(6\times 6\right)+\left(8\times 6\right)$

  $\Rightarrow$ Total weekly earnings $=0+36+24+0+12+36+48$

  $\Rightarrow$ Total weekly earnings $=\$156$

Therefore,

Total Weekly earnings of Amada $=\$156$

c.

To determine

To find: How many more hours Michael worked than Amanda.

Answer to Problem 17STP

Michael works $6$ hours more than Amanda.

Explanation of Solution

Given information:

Amanda earns $\$6$ per hour.

Amanda’s hours at her summer job for one week are listed in the table.

Michael earns $\$6$ per hour.

Michael total weekly earnings $=\$192$

Given

Amanda earns $\$6$ per hour.

Amanda’s hours at her summer job for one week are listed in the table.

Number of hours she works on Sunday $=0$

Number of hours she works on Monday $=6$

Number of hours she works on Tuesday $=4$

Number of hours she works on Wednesday $=0$

Number of hours she works on Thursday $=2$

Number of hours she works on Friday $=6$

Number of hours she works on Saturday $=8$

Therefore,

Total hours Amanda works $=0+6+4+0+2+6+8=26$ hours

Michael earns $\$6$ per hour.

Michael total weekly earnings $=\$192$

Let $x$ be number of hours worked by Michael.

We know

Total weekly earnings $=$ Number of hours worked $\times$ Earnings for each hour

  $\begin{array}{l}\Rightarrow 192=x\times 6\\ \Rightarrow 6x=192\\ \Rightarrow \frac{6x}{6}=\frac{192}{6}\\ \Rightarrow x=\frac{192}{6}\\ \Rightarrow x=32\end{array}$

Therefore,

Michael works $32$ hours

Whereas Amanda works $26$ hours

Therefore,

Difference $=32-26=6$

Therefore,

Michael works $6$ hours more than Amanda.