Q63. - Algebra 2

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.

Step-by-Step Solution

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 1 - 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

Step 2 - Write first expression

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

So her total earning A  in given week is

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

Step 3 - 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

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