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Question

Michele has $55 after 2 weeks of saving money. She plans to have $105 after 7 weeks of saving.

Which equation matches this scenario?

(1 point)
Responses

10x+7y=55
10 x plus 7 y is equal to 55

y−55=10(x−2)
y minus 55 is equal to 10 times open paren x minus 2 close paren

y+7=10(x+2)
y plus 7 is equal to 10 times open paren x plus 2 close paren

y=7x+55

1 answer

To formulate the equation that matches Michele's savings scenario, we first need to determine the relationship between the weeks and the amount of money she has saved.

  1. Michele has $55 after 2 weeks.
  2. Michele plans to have $105 after 7 weeks.

From these points, we can derive the following:

  • The change in amount saved from week 2 to week 7 is \( 105 - 55 = 50 \).
  • The number of weeks between the two observations is \( 7 - 2 = 5 \) weeks.

Now we can calculate the weekly savings rate:

  • Weekly savings = Total change in savings / Number of weeks = \( 50 / 5 = 10 \).

This indicates that Michele saves $10 per week.

Now, we can express the amount of money Michele has in terms of the number of weeks \( x \) (starting from week 2):

  1. Let \( y \) be the total amount of savings after \( x \) weeks.
  2. We know she starts at $55 after 2 weeks and adds $10 for each additional week thereafter.

So, after \( x \) weeks, we could express her savings as: \[ y = 10(x - 2) + 55 \]

Rearranging this, we get: \[ y - 55 = 10(x - 2) \]

This matches the second option given in the question:

y−55=10(x−2)

Therefore, the correct equation that matches this scenario is:

y−55=10(x−2)