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Patty is a customer service representative for a company. She earns [tex]$\$ 18$[/tex] an hour, plus an additional [tex]$\[tex]$ 2.50$[/tex][/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]$\$ 750$[/tex] this week, which inequality could she solve to find the number of surveys, [tex]$s[tex]$[/tex], she needs her customers to complete this week?

A. [tex]$[/tex]20.5 s > 750$[/tex]

B. [tex]$18(2.5 s + 38) \geq 750$[/tex]

C. [tex]$18(38) + 2.5 s \geq 750[tex]$[/tex]

D. [tex]$[/tex]18(s + 2.5) > 750$[/tex]



Answer :

GinnyAnswer
To determine which inequality Patty needs to solve to find the number of surveys her customers need to complete, we start by calculating her total earnings based on the given information:

1. Hourly Wage and Hours Worked:
- Patty earns [tex]$18 per hour. - She plans to work 38 hours. Her earnings from hours worked can be calculated as: \[ 18 \text{ dollars/hour} \times 38 \text{ hours} = 684 \text{ dollars} \] 2. Additional Earnings from Surveys: - Patty earns an additional $[/tex]2.50 for each survey her customers complete.
- Let [tex]\( s \)[/tex] be the number of surveys completed.

Her additional earnings from the surveys are:
[tex]\[ 2.5 \text{ dollars} \times s \][/tex]

3. Desired Total Earnings:
- Patty wants to earn at least $750 this week.

Combining her earnings from hours worked and surveys, we set up the inequality:
[tex]\[ \text{Earnings from hours} + \text{Earnings from surveys} \geq 750 \][/tex]
Substituting the values, we get:
[tex]\[ 684 + 2.5s \geq 750 \][/tex]

4. Simplify the Inequality:
[tex]\[ 18(38) + 2.5s \geq 750 \][/tex]

So, the correct inequality Patty needs to solve to find out how many surveys her customers need to complete is:
[tex]\[ C. 18(38) + 2.5s \geq 750 \][/tex]

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