To figure out which inequality Patty should solve to determine the number of surveys, [tex]\( s \)[/tex], she needs her customers to complete, let's break down her total earnings and arrange it in the form of an inequality.
1. Calculate Patty's earnings from her hours worked:
- Patty earns [tex]\( \$ 18 \)[/tex] per hour.
- This week she plans to work 38 hours.
- Her earnings from hours worked are:
[tex]\[
\text{Earnings from work} = 18 \times 38
\][/tex]
2. Calculate Patty's additional earnings from completed surveys:
- Patty earns an additional [tex]\( \$ 2.50 \)[/tex] for each completed survey.
- If she needs her customers to complete [tex]\( s \)[/tex] surveys, her earnings from surveys would be:
[tex]\[
\text{Earnings from surveys} = 2.5 \times s
\][/tex]
3. Compute the total earnings Patty needs:
- Patty wants her total earnings to be at least [tex]\( \$ 750 \)[/tex].
- Total earnings are the sum of earnings from hours worked and survey bonuses:
[tex]\[
\text{Total earnings} = 18 \times 38 + 2.5 \times s
\][/tex]
- We require this total to be at least [tex]\( \$ 750 \)[/tex], so we set up the inequality:
[tex]\[
18 \times 38 + 2.5 \times s \geq 750
\][/tex]
4. Match the inequality to the given choices:
- The correct inequality that Patty should solve to find the number of surveys is:
[tex]\[
18 \times 38 + 2.5 \times s \geq 750
\][/tex]
This corresponds to the option:
B. [tex]\( 18(38) + 2.5s \geq 750 \)[/tex]
