Question

Michele has $50. She plans to save $15 per week until she has a total of $230.

Which equation matches this scenario?

Responses
y= - 15x + 50
y= 50x + 15
y= 110 = 15 (x - 4)
15x + 50y = 230

Answer 1

In this scenario, Michele starts with $50 and saves $15 per week. We want to find an equation that models her total savings over time until she reaches $230.

Let's define the variables:
- \( y \) is the total amount saved.
- \( x \) is the number of weeks.

The total amount saved after \( x \) weeks can be expressed as:

\[ y = 50 + 15x \]

We can rearrange it to form the equation where you subtract 50 from both sides:

\[ y - 50 = 15x \]

Hence, if we want to express it in the standard form where it equals $230:

\[ 50 + 15x = 230 \]

Now solve for \( x \):

\[
15x = 230 - 50
\]
\[
15x = 180
\]
\[
x = 12
\]

This shows she reaches the target of $230 after 12 weeks, starting from $50 and adding $15 each week.

From the provided responses, however, let's check the options:

1. \( y= -15x + 50 \) (Does not match)
2. \( y= 50x + 15 \) (Does not match)
3. \( y= 110 = 15 (x - 4) \) (Not in standard form, does not match)
4. \( 15x + 50y = 230 \) (This is not the correct representation either)

None of the options directly match the expected equation. The correct form based on our analysis is \( y = 15x + 50 \).

However, if we flip our approach and focus solely on evaluating the fourth option for correctness:

The fourth option \( 15x + 50y = 230 \) cannot yield a correct interpretation of the linear growth Michele's savings because \( y \) cannot be multiplied by \( 50 \) in this context as \( 15x + 50y = 230 \) suggests a relationship between two unknowns in different contexts.

In conclusion, the best approach would be to write the functional equation \( y = 15x + 50 \) but need to clarify that the provided options do not correctly represent the scenario described.