Math Problem Statement

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?

Solution

Let's define the variables and set up the inequality:

  • Let the cost of one gift card be xx.
  • Russel is buying 3 identical gift cards, so the total cost is 3x3x.
  • He wants the total cost to be within $2 of $60. This means the total cost can be no more than $2 above or below $60.

This translates to the following inequality:

3x602|3x - 60| \leq 2

This absolute value inequality represents the total cost being within $2 of $60. To break this down into two inequalities without the absolute value:

23x602-2 \leq 3x - 60 \leq 2

Now, add 60 to all sides of the inequality:

583x6258 \leq 3x \leq 62

Thus, the inequality representing this situation is:

583x6258 \leq 3x \leq 62

Would you like more details or have any questions?

Here are 5 related questions to explore:

  1. How do you solve absolute value inequalities in general?
  2. What if Russel wanted to buy 4 gift cards instead?
  3. How would the inequality change if the range was $5 instead of $2?
  4. What happens if Russel wants the total cost to be exactly $60?
  5. How would the inequality change if the price of each gift card varies by tax?

Tip: When dealing with absolute value inequalities, remember that they split into two separate inequalities, one positive and one negative.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Absolute Value

Formulas

|3x - 60| ≤ 2

Theorems

Absolute Value Inequalities

Suitable Grade Level

Grades 6-8