Practice Solving Inequality Word Problems

Strategy

The storage Nancy has on her phone plus the storage she buys on memory cards needs to be at least ‍1000GB. We can represent this with an inequality whose structure looks something like this:

\(\left(  \text{amount on phone} \right) + \left(  \text{amount from cards} \right) [\leq \text{or} \geq] \,1000\)

Then, we can solve the inequality for \(C\) to find how many memory cards Nancy needs to buy.

1) Which inequality?

• Nancy already has ‍105GB available on her phone.

• Each card has ‍256GB of storage, and ‍\(C\) represents the number of cards she buys, so the amount of memory she buys on cards is \(256C\)

• The amount of memory she has available on her phone combined with the amount of memory she buys from cards must be greater than or equal to 1000GB.

\(\begin{aligned}
\left(  {\text{amount on phone}} \right) &+ \left(  {\text{amount from cards}} \right) [\leq \text{or} \geq] \,1000
\\\\
{105}&+{256C} {\geq} 1000
\end{aligned}\)

2) How many cards does Nancy need?

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

\(\begin{aligned}
105+256C &\geq 1000 &&\text{Subtract }105
\\\\
256C &\geq 895 &&\text{Divide by }256
\\\\
C &\geq 3.496 \dots
\end{aligned}\)

Since she can't buy a partial memory card, Nancy needs to buy ‍4 cards. And each card costs ‍$10, so buying ‍4 cards costs ‍\(4 \cdot \$10=\$40\).

Answers

1. The inequality that describes this scenario is \(105+256C \geq 1000\)

2. Nancy needs to spend ‍$40 on memory cards.