Question
There are 6 quarters in a jar. Jill adds 2 quarters to the jar every day. Which linear equation represents the total amount of quarters in the jar after \( x \) days?
Ask by Dawson Pope. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The total number of quarters after \( x \) days is \( Q = 6 + 2x \).
Solution
To find the linear equation that represents the total amount of quarters in the jar after \( x \) days, we can follow these steps:
1. **Identify the initial amount of quarters**:
- There are initially 6 quarters in the jar.
2. **Identify the rate of change**:
- Jill adds 2 quarters to the jar every day.
3. **Define the variable**:
- Let \( x \) represent the number of days.
4. **Formulate the equation**:
- The total amount of quarters after \( x \) days can be expressed as the initial amount plus the amount added over \( x \) days.
- The amount added after \( x \) days is \( 2x \) (since she adds 2 quarters each day).
Putting this all together, the total amount of quarters \( Q \) in the jar after \( x \) days can be represented by the equation:
\[
Q = 6 + 2x
\]
This is the linear equation that represents the total amount of quarters in the jar after \( x \) days.
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Simplify this solution Mind Expander
The total number of quarters in the jar can be represented by the equation \( y = 6 + 2x \), where \( y \) is the total number of quarters after \( x \) days. The equation starts with the initial 6 quarters and adds 2 for each day that passes. You can easily visualize this by imagining Jill's daily routine. Each day, as she adds those shiny quarters, the total grows in a steady and predictable way—just like how your savings might grow with careful deposits! So if you wanted to calculate, say, how many quarters you'd have after 5 days, just plug 5 into \( x \) and see the magic unfold!
