To determine the inequality that Patty could use to find the number of surveys, [tex]$s$[/tex], she needs her customers to complete this week in order to earn at least [tex]$\$[/tex]750[tex]$, we can proceed as follows:
1. Calculate the income from hourly wage:
Patty earns $[/tex]\[tex]$18$[/tex] per hour, and she plans to work 38 hours this week. Therefore, her earnings from just working can be calculated as:
[tex]\[
18 \times 38
\][/tex]
Performing the multiplication,
[tex]\[
18 \times 38 = 684
\][/tex]
So, Patty will earn [tex]$\$[/tex]684[tex]$ from her hourly work.
2. Set up the inequality for total earnings:
Let \( s \) be the number of surveys completed by her customers. Patty earns an additional $[/tex]\[tex]$2.50$[/tex] per survey. The total additional earnings from surveys can be written as:
[tex]\[
2.5 \times s
\][/tex]
3. Combine Patty's earnings from hours worked and surveys:
Patty's total earnings should be at least [tex]$\$[/tex]750[tex]$. Therefore, the total earnings (from hours worked and surveys) can be written as:
\[
684 + 2.5 \times s \geq 750
\]
Thus, the inequality that represents the minimum number of surveys Patty needs her customers to complete in order to earn at least $[/tex]\[tex]$750$[/tex] is:
[tex]\[
684 + 2.5s \geq 750
\][/tex]
From the given options, the correct inequality is:
[tex]\[
B. 18(38) + 2.5s \geq 750
\][/tex]
