Russel wants to buy 3 identical gift cards. He wants to make sure his total cost is no more than $2 above or below $60. Which of the following inequalities represents this situation?

A. |3c − 60| ≤ 2
B. |60 + 3c| ≤ 2
C. |3c − 2| ≤ 60
D. |3c + 2| ≤ 60

1 answer

To model the situation where Russel wants his total cost for 3 identical gift cards (let's denote the cost of each gift card as \(c\)) to be no more than $2 above or below $60, we first need to capture how much he desires to spend.

The total cost of 3 gift cards is \(3c\). Russel wants this total cost to be between $58 and $62, inclusive. We can express this requirement mathematically with the following inequality:

\[ 58 \leq 3c \leq 62 \]

This can be rearranged into a single absolute value inequality. To do that, we can rewrite it as:

\[ |3c - 60| \leq 2 \]

This expression captures the idea that the distance of \(3c\) from $60 should be at most $2.

Thus, the correct option that represents the situation is:

A. \(|3c - 60| \leq 2\)