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 .
- Russel is buying 3 identical gift cards, so the total cost is .
- 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:
This absolute value inequality represents the total cost being within $2 of $60. To break this down into two inequalities without the absolute value:
Now, add 60 to all sides of the inequality:
Thus, the inequality representing this situation is:
Would you like more details or have any questions?
Here are 5 related questions to explore:
- How do you solve absolute value inequalities in general?
- What if Russel wanted to buy 4 gift cards instead?
- How would the inequality change if the range was $5 instead of $2?
- What happens if Russel wants the total cost to be exactly $60?
- 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