Question

Michele has $25. She plans to save $10 per week until she has a total of $75.

Which equation matches this scenario?

(1 point)
Responses

y - 55 = 10(x - 3)
y - 55 = 10(x - 3)

10x + y = 25
10x + y = 25

y + 4 = 10 (x - 65)
y + 4 = 10 (x - 65)

y = 10x - 25

Answer 1

To find the correct equation that matches Michele’s scenario, we need to define the variables and how they relate to each other:

Let:
- \( y \) be the total amount of money Michele has after \( x \) weeks.
- Initially, she has $25.
- She saves $10 each week.

Her total amount after \( x \) weeks can be represented as:

\[
y = 25 + 10x
\]

We need to find the equation that satisfies the condition that she wants to save until she has a total of $75.

Setting \( y = 75 \), we have:

\[
75 = 25 + 10x
\]
\[
50 = 10x
\]
\[
x = 5
\]

This means that after 5 weeks, she will have saved enough money to reach $75.

Now converting the equation \( y = 25 + 10x \) to match any of the provided forms:

Subtract 25 from both sides to obtain:

\[
y - 25 = 10x
\]

This rearrangement does not exactly match any of the options, so let's analyze the provided responses:

1. **\( y - 55 = 10(x - 3) \)**: This would imply \( y = 10x - 30 + 55 = 10x + 25 \), which matches our derived formula.

2. **\( 10x + y = 25 \)**: Rearranged, this gives \( y = 25 - 10x \), which does not match.

3. **\( y + 4 = 10(x - 65) \)**: Rearranged, this gives \( y = 10x - 650 - 4\), which does not match.

4. **\( y = 10x - 25 \)**: This does not match because it suggests she starts with a negative amount (\(-25\)).

Based on the analysis, the correct equation that matches Michele’s savings scenario is:

**\( y - 55 = 10(x - 3) \)**.