Michele had $55 after 2 weeks of saving money. She plans to have $105 after 7 weeks of saving.which equation matches this scenario?

Question

y = 55 = 10 (x - 2)
y = 7x + 55
10x + 7y = 55
y + 7 = 10 (x + 2)

Answer 1

To determine which equation matches the scenario, we should first identify the relationship between weeks and the total amount saved.

1. Identify initial amount and rate of saving:

   • After 2 weeks, Michele has $55.
   • She aims to have $105 after 7 weeks.

2. Calculate the total amount saved over the 5 weeks (from week 2 to week 7):

   • $105 (after 7 weeks) - $55 (after 2 weeks) = $50 over 5 weeks.
   • Therefore, the rate of saving is \(\frac{50}{5} = 10\) dollars per week.

3. Formulate the general equation:

   • Let \(x\) be the number of weeks.
   • The amount saved can be modeled with a linear equation. After 2 weeks, she has $55, and for each additional week, she adds $10.
   • The equation in point-slope form can be constructed: After \(x\) weeks, her amount \(y\) is represented as: \[ y = 10(x - 2) + 55 \]
   • This can be rearranged to: \[ y = 10x - 20 + 55 \] \[ y = 10x + 35 \]
   • It matches the form but we want the form in the choices.

4. Choices evaluation:

   • Let's evaluate the given options based on the identified elements:
     • Choice 1: \(y = 55 + 10(x - 2)\): This matches our structure. After 2 weeks, \(x = 2\), \(y = 55\).
     • Choice 2: \(y = 7x + 55\): Doesn't fit the pattern or data.
     • Choice 3: \(10x + 7y = 55\): Not applicable.
     • Choice 4: \(y + 7 = 10(x + 2)\): Doesn’t fit the structure.

Thus, the equation that matches this scenario is:

\(y = 55 + 10(x - 2)\).