Question

WORK

Use the information below and in the table.

Andrea works as a hostess in a restaurant and is paid every two weeks.

63. If Andrea earns$\$6.50$ an hour, illustrate the Distributive Property by writing two expressions representing Andrea’s pay last week.

Short answer

Two expressions to represent the given situation are

$\left(0\times 6.50\right)+\left(4.5\times 6.50\right)+\left(0\times 6.50\right)+\left(4.25\times 6.50\right)+\left(5.25\times 6.50\right)+\left(6.5\times 6.50\right)+\left(5\times 6.50\right)$ and $\left(0+4.5+0+4.25+5.25+6.5+5.0\right)\times 6.50$

Step-by-step solution

- Observations from image

From given image, number of hours worked on

• Monday is 0,
• Tuesday is 4.5,
• Wednesday is 0,
• Thursday is 4.25,
• Friday is 5.25,
• Saturday is 6.5, and
• Sunday is 5.0

- Write first expression 

Since, person A earns $\$6.50$per hour.

So her total earning A in given week is

$A=\left(0\times 6.50\right)+\left(4.5\times 6.50\right)+\left(0\times 6.50\right)+\left(4.25\times 6.50\right)+\left(5.25\times 6.50\right)+\left(6.5\times 6.50\right)+\left(5\times 6.50\right)$

- Write second expression

For any real numbers a, b, and c distributive property is

$a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$

For second expression, use distributive property in first expression

$A=\left(0+4.5+0+4.25+5.25+6.5+5.0\right)\times 6.50$