Question

Michele had $55 after 2 weeks of saving money. She plans to have $105 after 7 weeks of saving.which equation matches this scenario?

y = 55 = 10 (x - 2)
y = 7x + 55
10x + 7y = 55
y + 7 = 10 (x + 2)

Answer 1

To determine which equation matches the scenario, we should first identify the relationship between weeks and the total amount saved.

1. **Identify initial amount and rate of saving**:
- After 2 weeks, Michele has $55.
- She aims to have $105 after 7 weeks.

2. **Calculate the total amount saved over the 5 weeks (from week 2 to week 7)**:
- $105 (after 7 weeks) - $55 (after 2 weeks) = $50 over 5 weeks.
- Therefore, the rate of saving is \(\frac{50}{5} = 10\) dollars per week.

3. **Formulate the general equation**:
- Let \(x\) be the number of weeks.
- The amount saved can be modeled with a linear equation. After 2 weeks, she has $55, and for each additional week, she adds $10.
- The equation in point-slope form can be constructed: After \(x\) weeks, her amount \(y\) is represented as:
\[
y = 10(x - 2) + 55
\]
- This can be rearranged to:
\[
y = 10x - 20 + 55
\]
\[
y = 10x + 35
\]
- It matches the form but we want the form in the choices.

4. **Choices evaluation**:
- Let's evaluate the given options based on the identified elements:
- **Choice 1**: \(y = 55 + 10(x - 2)\): This matches our structure. After 2 weeks, \(x = 2\), \(y = 55\).
- **Choice 2**: \(y = 7x + 55\): Doesn't fit the pattern or data.
- **Choice 3**: \(10x + 7y = 55\): Not applicable.
- **Choice 4**: \(y + 7 = 10(x + 2)\): Doesn’t fit the structure.

Thus, the equation that matches this scenario is:

**\(y = 55 + 10(x - 2)\)**.