Math Problem Statement
Ricky wants to buy a video camera that costs $850. He already has $300 to spend on it and can afford to save $40 per week towards its purchase. Which of the following inequalities can be solved to find t, the number of weeks that Ricky must save to afford the camera? A.40t – 300 ≥ 850 B.300 + 40t ≥ 850 C.40 + 300t ≥ 850 D.300t + 40t ≥ 850
Solution
Let's break down the problem step by step:
- The total cost of the video camera is $850.
- Ricky already has $300 saved.
- He can save $40 per week.
We need to find the number of weeks, t, it will take for him to save enough money to buy the camera. To set up an inequality, we know the total amount he has after t weeks will be his initial amount ($300) plus the amount he saves weekly ($40 per week).
Thus, the inequality would be: This represents the sum of his initial savings and the amount he saves over t weeks, which must be greater than or equal to $850.
The correct inequality is B. 300 + 40t ≥ 850.
Would you like a detailed explanation on how to solve the inequality? Here are 5 related questions:
- How do you solve the inequality ?
- What if Ricky can only save $30 per week? How does the inequality change?
- What if the camera cost was $1000 instead of $850?
- How would the inequality change if Ricky already had $400 saved?
- What would the inequality look like if Ricky was saving for multiple items?
Tip: When setting up inequalities for real-world problems, always check if you’re adding or multiplying based on whether the amount is a lump sum or a recurring weekly/monthly savings.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Linear Equations
Formulas
300 + 40t ≥ 850
Theorems
Properties of inequalities
Suitable Grade Level
Grades 6-8
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