Math Problem Statement

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Tara starts with $80 in her bank account. She takes out $15 each week to spend. Based on the table provided, what is the equation representing her account balance after x weeks?

Solution

The problem shows Tara starting with $80 in her bank account and withdrawing $15 each week, which reduces her balance. The table lists the number of weeks xx and the corresponding account balance yy.

To form the equation, we can observe that:

  • The starting balance at x=0x = 0 is $80.
  • Tara withdraws $15 every week, which means her balance decreases by $15 for each additional week.

The equation for this scenario can be written as: y=8015xy = 80 - 15x

Now, for the equation in the blank format: The left side will be yy, and the right side will be 8015x80 - 15x, so: y=8015xy = 80 - 15x

Does this clarify things for you? Let me know if you'd like further details!

Here are 5 related questions to consider:

  1. What would the equation be if Tara withdrew $20 each week instead of $15?
  2. How many weeks will it take for Tara's account to reach $0?
  3. What is the rate of change in her account balance per week?
  4. Can you express the number of weeks xx as a function of the account balance yy?
  5. How would the equation change if Tara started with $100 instead of $80?

Tip: To find the equation of a line from a table, look for the initial value and the rate of change (slope).

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra

Formulas

y = 80 - 15x

Theorems

Slope-Intercept Form (y = mx + b)

Suitable Grade Level

Grade 7-8