Let's define the variables in the scenario to formulate the equation correctly:
- Let \( y \) be the total amount of money Michele has after \( x \) weeks.
- Michele starts with $25 and saves $10 each week.
After \( x \) weeks, the total amount \( y \) can be expressed as:
\[ y = 25 + 10x \]
Michele wants to save until she has a total of $75. We can set up the equation:
\[ y = 75 \]
Now substituting this into our earlier equation:
\[ 75 = 25 + 10x \]
To match this with the provided equations, we need to rearrange it. Let's solve for \( x \):
- Subtract 25 from both sides:
\[ 75 - 25 = 10x \]
\[ 50 = 10x \]
- Divide both sides by 10:
\[ x = 5 \]
Now, none of the provided equations seem to match the direct equation we created. However, we can interpret them to see which one matches our calculations correctly.
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\( y - 55 = 10(x - 3) \) can be rewritten as \( y = 10x + 25 \), which is not what we need.
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\( 10x + y = 25 \) can be rearranged but does not represent our scenario correctly.
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\( y + 4 = 10(x - 65) \) will also not represent our scenario correctly.
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\( y = 10x - 25 \) can be rearranged to \( y = 10x + 25 \), which doesn't represent our funds accurately.
None of these equations perfectly reflect the scenario we derived \( y = 25 + 10x \). However, since \( y \) should be $75 when \( x = 5 \), the most suitable representation of the scenario in terms of the goal is actually none of the provided equations directly.
Instead, the correct representation for Michele's plan in a simple linear form is:
\[ y = 10x + 25. \]
This matches what we established. If forced to select from the options, none is suitable without alteration. If you have to choose one for similarity, none reflect the total goal accurately.
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