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.40 + 300t ≥ 850 B.40t – 300 ≥ 850 C.300 + 40t ≥ 850 D.300t + 40t ≥ 850

Solution

We are tasked with finding the inequality that can be solved to determine how many weeks Ricky must save in order to afford a video camera costing $850.

Here's a breakdown:

  • Ricky has $300 already.
  • He saves an additional $40 per week.
  • The total amount he needs is $850.

The inequality should represent the sum of his initial amount ($300) and the additional savings per week ($40 times the number of weeks, t), which needs to be at least $850.

This leads us to the equation: 300+40t850300 + 40t \geq 850

This represents the total amount Ricky will have after saving for t weeks, which should be greater than or equal to $850.

The correct inequality is: C. 300+40t850\boxed{C. \ 300 + 40t \geq 850}

Would you like me to show the step-by-step solution for solving this inequality, or do you have any other questions?


Here are 5 related questions:

  1. How would you solve the inequality 300+40t850300 + 40t \geq 850 to find the value of tt?
  2. What would the inequality look like if Ricky saved $50 per week instead?
  3. If the camera cost $950, how would the inequality change?
  4. How many weeks would Ricky need if he had only $200 saved initially?
  5. What if Ricky increased his weekly savings by $10 after 5 weeks?

Tip: When dealing with inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Linear Equations

Formulas

Linear inequality: 300 + 40t ≥ 850

Theorems

Basic properties of inequalities

Suitable Grade Level

Grades 6-8