Practice Solving Inequality Word Problems

Strategy

Jacque wants the delivery fee plus the cost of the pizzas to be under $60. We can represent this with an inequality whose structure looks something like this:

\(\left(  \text{delivery fee} \right) + \left(  \text{cost of pizzas} \right) [ < \text{or} > ] \,60\)

Then, we can solve the inequality for \(P\) to find how many pizzas Jacque can afford.

1) Which inequality?

• The delivery fee is ‍$7.50.

• Each pizza costs ‍$14, and ‍\(P\) represents the number of pizzas Jacque buys, so the cost of pizzas is ‍\({14 \cdot P}\).

• Jacque wants the delivery fee plus the cost of the pizzas to be under ‍$60, so the total must be less than $60.
  

\(\begin{aligned}
\left(  {\text{delivery fee}} \right) &+ \left(  {\text{cost of pizzas}} \right) [ < \text{or} > ] \,60
\\\\
{7.50}&+{14P} { < } 60
\end{aligned}\)

2) How many pizzas can Jacque afford?

Let's solve our inequality for \(P\):

\(\begin{aligned}
7.50+14P &< 60 &&\text{Subtract }7.50
\\\\
14P &< 52.50 &&\text{Divide by }14
\\\\
P &< 3.75
\end{aligned}\)

Since she can't buy partial pizzas, Jacque can afford at most ‍3 pizzas. And each pizza has ‍8 slices, so buying ‍3 pizzas gets her ‍\(3 \cdot 8=24\) slices.

Answers

1. The inequality that describes this scenario is \(7.50+14P < 60\)

2. Jacque can afford at most 24 slices.