Practice Solving Inequality Word Problems

Strategy

The flour Sergei already has plus the flour he buys must be greater than or equal to 175 kilograms. We can represent this with an inequality whose structure looks something like this:

\(\left(  \text{amount he has} \right) + \left(  \text{amount he buys} \right) [\leq \text{or} \geq] \,175\)

Then, we can solve the inequality for \(F\) to find how many bags of flour Sergei needs to buy.

1) Which inequality?

• Sergei already has 34 kilograms of flour.

• Each bag of flour contains 23 kilograms, and ‍\(F\) represents the number of bags he buys, so the amount of flour he buys is \({23 \cdot F}\).

• The amount of flour he has combined with the amount of flour he buys must be greater than or equal to 175 kilograms.

\(\begin{aligned}
\left(  {\text{amount he has}} \right) &+ \left(  {\text{amount he buys}} \right) [\leq \text{or} \geq] \,175
\\\\
{34}&+{23F} {\geq} 175
\end{aligned}\)

2) How many bags does Sergei need?

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

\(\begin{aligned}
34+23F &\geq 175 &&\text{Subtract }34
\\\\
23F &\geq 141 &&\text{Divide by }23
\\\\
F &\geq 6.13 \dots
\end{aligned}\)

Since he can't buy a partial bag of flour, Sergei needs to buy 7 bags.

Answers

1. The inequality that describes this scenario is \(34+23F \geq 175\)

2. Sergei needs to buy 7 bags to get the amount of flour he needs.