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:
-
\( y - 55 = 10(x - 3) \): This would imply \( y = 10x - 30 + 55 = 10x + 25 \), which matches our derived formula.
-
\( 10x + y = 25 \): Rearranged, this gives \( y = 25 - 10x \), which does not match.
-
\( y + 4 = 10(x - 65) \): Rearranged, this gives \( y = 10x - 650 - 4\), which does not match.
-
\( y = 10x - 25 \): 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:
\( y - 55 = 10(x - 3) \).
1 answer