Question

Michele has $55 after 2 weeks of saving money. She plans to have $105 after 7 weeks of saving.

Which equation matches this scenario?

(1 point)

y − 55 = 10 ( x − 2 )

y = 7x + 55


10x + 7y = 55


y + 7 = 10 ( x + 2 )

Answer 1

To find an equation that matches Michele's saving scenario, we can determine a few key components from the data given:

1. After 2 weeks (x = 2), Michele has $55 (y = 55).
2. After 7 weeks (x = 7), Michele plans to have $105 (y = 105).

From this, we can calculate Michele's weekly savings:

The difference in weeks from 2 to 7 is 5 weeks, and the difference in her savings from $55 to $105 is:
\[
105 - 55 = 50.
\]
So, her savings per week is:
\[
\text{Savings per week} = \frac{50}{5} = 10.
\]

Now we can create a linear equation based on this information. The general form of a linear equation for savings can be represented as:
\[
y = mx + b,
\]
where \(m\) is the slope (weekly savings), and \(b\) is the initial amount saved after some time.

Here, \(m = 10\) (she saves $10 a week), and we know that after 2 weeks she has $55, which can help us find \(b\).

Using the point (2, 55):
\[
55 = 10(2) + b \\
55 = 20 + b \\
b = 55 - 20 \\
b = 35.
\]

So the equation for her total savings over x weeks is:
\[
y = 10x + 35.
\]

Now, to match this with the provided equations:

1. \(y - 55 = 10(x - 2)\)
- Rearranging this gives:
\[
y = 10(x - 2) + 55 \\
y = 10x - 20 + 55 \\
y = 10x + 35.
\]
This equation is equivalent to what we derived.

2. \(y = 7x + 55\) is incorrect as slope does not match.

3. \(10x + 7y = 55\) is not in the correct form.

4. \(y + 7 = 10(x + 2)\) is not equivalent either.

Therefore, the correct answer is:
\[
\boxed{y - 55 = 10(x - 2)}.
\]