Charlotte works in a calling center making appointments for a local lawn care service. She earns $40 each full workday plus an additional $2 for each appointment that she schedules. Today, Charlotte needs to earn at least $75. Write an inequality to describe this situation. In two or more complete sentences, describe the solution set of this inequality and what it means for Charlotte.

The 2x is from her earning $2 per appointment. If she makes x of them, then she earns 2x dollars. This is on top of the $40 from working the full day.

She wants to earn at least $75. This means she wants to earn $75 or more.

This means,

[tex]y \ge 75\\\\2x+40 \ge 75\\\\2x \ge 75-40\\\\2x \ge 35\\\\x \ge \frac{35}{2}\\\\x \ge 17.5[/tex]

Since x is the number of appointments, and we can't have a fractional number of appointments, we must round up to x = 18. This is the lowest number of appointments she can do and earn $75 or larger.

If x = 17, then

y = 2x+40 = 2*17+40 = 34+40 = 74

which is not 75 or larger

But if x = 18, then

y = 2x+40 = 2*18+40 = 36+40 = 76

which is larger than 75, so we've cleared the hurdle.

We can say the solution set is [tex]x \ge 18[/tex] where x is a whole number. So she could book x = 18, x = 19, x = 20, x = 21, etc as the number of appointments to reach her goal.

In summary, she must schedule at least 18 appointments to earn $75 or more.

dummyproper dummyproper · Answer 2 · 2020-12-02T23:39:21+01:00

Since she makes $2 for every appointment she makes we would need to use 40+2n so she would get $2 per appointment no matter how many appointments she makes. Also, we wouldn't use an equal sign because they didn't say she needed to earn exactly $75. They said she needed to earn "at least" $75. At least means equal to or greater than ≥. So the inequality would be 2n+40≥75. PRO TIP: Any time it asks you to write an inequality you will use either <, >, ≤, or ≥ not an =.An equation uses =, an inequality uses the other symbols