Question

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

Which equation matches this scenario?


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

Answer 1

To represent Michele's savings plan with an equation, we can define the following:

- Let \( y \) represent the total amount of money Michele has.
- Let \( x \) represent the number of weeks she saves.

Michele starts with $50 and saves $15 each week. Therefore, the relationship can be expressed as:

\[
y = 15x + 50
\]

Now let's check the provided options:

1. \( y = 50x + 15 \) - This is incorrect because it has the wrong coefficients.
2. \( y = -15x + 50 \) - This is incorrect because it represents a decreasing amount rather than an increasing amount.
3. \( y - 110 = 15(x - 4) \) - This can be transformed into the slope-intercept form but doesn't directly represent the scenario.
4. \( 15x + 50y = 230 \) - This represents a different relationship, combining variables incorrectly.

None of the equations exactly match the derived equation \( y = 15x + 50 \).

However, if we need to rewrite the best matching option, we can work with the equation \( y - 110 = 15(x - 4) \).

Let's expand that equation:
\[
y - 110 = 15x - 60
\]
\[
y = 15x + 50
\]

So, while it isn't in the basic form I've derived, it ultimately represents the same relationship Michele's savings plan indicates. Thus, \( y - 110 = 15(x - 4) \) is the best match given this context, even though it doesn't directly correspond to the simple linear form.