Math Problem Statement

Helen had $330 in her savings account when Vince opened a savings account with zero dollars. Helen deposited $30 into her account each week for x weeks, and Vince deposited $50 into his account each week for x weeks. The accounts did not earn interest. Which inequality represents this situation when the amount of money in Helen's account was greater than the amount of money in Vince's account?

Solution

The question asks for the inequality that represents when the amount in Helen's account is greater than Vince's account.

Helen's Account:

  • She starts with $330.
  • Deposits $30 each week for xx weeks.
  • The total in her account after xx weeks is: 330+30x330 + 30x

Vince's Account:

  • Starts with $0.
  • Deposits $50 each week for xx weeks.
  • The total in his account after xx weeks is: 50x50x

The Inequality:

We are asked to find when Helen's account is greater than Vince's account. So, the inequality is: 330+30x>50x330 + 30x > 50x

This matches the option 330+30x>50x330 + 30x > 50x.

Let me know if you'd like more details on solving this inequality or have any questions. Here are some follow-up questions:

  1. How do we solve inequalities involving variables?
  2. What happens if we swap the inequality direction?
  3. How would the situation change if Vince had a starting balance?
  4. Can inequalities represent real-world constraints in other contexts?
  5. How do you graph solutions of inequalities on a number line?

Tip: When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign!

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities

Formulas

Helen's total: 330 + 30x
Vince's total: 50x

Theorems

Properties of Inequalities

Suitable Grade Level

Grades 7-9