Practice Solving Inequality Word Problems

Strategy

The money Alonso spends on eggs plus the money he spends on sugar must be less than or equal to ‍$55. We can represent this with an inequality whose structure looks something like this:

$$\left(  \text{money on eggs} \right) + \left(  \text{money on sugar} \right) [\leq \text{or} \geq] \,55$$

Then, we can solve the inequality for $$S$$ to find how many boxes of sugar Alonso can afford.

1) Which inequality?

• The package of eggs costs ‍$2.75, and Alonso needs one package, so he's spending ‍$2.75on eggs.

• Each box of sugar costs ‍$11.50, and ‍$$S$$ represents the number of boxes of sugar he buys, so he's spending ‍$${11.50 \cdot S}$$ on sugar.

• The combined amount of money he spends on eggs and sugar must be less than or equal to $55.

$$\begin{aligned}
\left(  {\text{money on eggs}} \right) &+ \left(  {\text{money on sugar}} \right) [\leq \text{or} \geq] \,55
\\\\
{2.75}&+{11.50S} {\leq} 55
\end{aligned}$$

2) How many bags does Sergei need?

Let's solve our inequality for $$S$$:

$$\begin{aligned}
2.75+11.50S &\leq 55 &&\text{Subtract }2.75
\\\\
11.50S &\leq 52.25 &&\text{Divide by }11.50
\\\\
S &\leq 4.54 \dots
\end{aligned}$$

Since he can't buy partial boxes of sugar, Alonso can afford at most ‍4 boxes of sugar.

Answers

1. The inequality that describes this scenario is $$2.75+11.50S \leq 55$$

2. After getting the eggs, Alonso can afford ‍4 boxes of sugar.