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Patty is a customer service representative for a company. She earns [tex]$\$[/tex]18[tex]$ an hour, plus an additional $[/tex]\[tex]$2.50$[/tex] each time one of her customers completes a company survey. This week, Patty plans to work 38 hours.

If Patty wants to earn at least [tex]$\$[/tex]750[tex]$ this week, which inequality could she solve to find the number of surveys, $[/tex]s[tex]$, she needs her customers to complete this week?

A. $[/tex]\quad 18(s+2.5) > 750[tex]$
B. $[/tex]18(38) + 2.5s \geq 750[tex]$
C. $[/tex]20.5s > 750[tex]$
D. $[/tex]18(2.5s + 38) \geq 750$



Answer :

GinnyAnswer
To determine the number of customer surveys, [tex]\( s \)[/tex], that Patty needs her customers to complete to earn at least [tex]\( \$750 \)[/tex] this week, we need to first calculate her earnings from her regular working hours and then account for the bonus from the completed surveys.

1. Calculate Patty's earnings from her regular working hours:
- Patty earns [tex]\( \$18 \)[/tex] per hour.
- She plans to work 38 hours this week.
- Her earnings from working hours are [tex]\( 18 \times 38 = 684 \)[/tex] dollars.

2. Set up the inequality to account for the survey bonus:
- Patty needs her total earnings (from working hours plus survey bonuses) to be at least [tex]\( \$750 \)[/tex].
- Each completed survey provides an additional [tex]\( \$2.50 \)[/tex].
- We need to find the inequality that represents this situation.

Let's represent the additional earnings from surveys as [tex]\( 2.5s \)[/tex], where [tex]\( s \)[/tex] is the number of completed surveys.

3. Combine these components in an inequality:
- Patty's total earnings should be at least [tex]\( \$750 \)[/tex].
- Her earnings from working hours plus earnings from surveys can be written as: [tex]\( 684 + 2.5s \geq 750 \)[/tex].

4. Identify the correct inequality:
- The correct inequality that represents this situation is [tex]\( 18(38) + 2.5s \geq 750 \)[/tex].

Therefore, the answer is:
B. [tex]\( 18(38) + 2.5s \geq 750 \)[/tex]

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