Question

14 of 1614 of 16 Items 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 y−55=10(x−2) y minus 55 is equal to 10 times open paren x minus 2 close paren y=7x+55 y is equal to 7 x plus 55 10x+7y=55 10 x plus 7 y is equal to 55 y+7=10(x+2)

Answer 1

The correct equation for Michele's savings plan is y = 55 + 10(x - 2), representing her total savings y after x weeks, taking into account her initial savings and her weekly savings rate.

Step-by-step explanation:

The student needs to find the linear equation that describes Michele's savings over time. She begins with $55 and in 2 weeks, wants to save a total of $105 after 7 weeks. To get the weekly savings amount, we subtract her initial savings from her goal and divide by the number of weeks left to save:

$105 - $55 = $50

Then we divide $50 by the 5 remaining weeks (7 weeks total - 2 weeks already saved).

$50 ÷ 5 = $10 per week

Thus, Michele saves $10 each week. To represent this as an equation with y as the total amount saved after x weeks, we start with her initial $55 and add $10 for each week beyond the initial 2 weeks:

y = 55 + 10(x - 2)

This linear equation matches the scenario as it accounts for both the initial savings and the constant weekly savings rate.

Answer 2

Michele saves $10 per week, starting with $55 after 2 weeks. The equation that represents her savings over time is y - 55 = 10(x - 2), where y is the total amount saved and x is the number of weeks.

Step-by-step explanation:

The scenario presented is that Michele has $55 after 2 weeks of saving and plans to have $105 after 7 weeks of saving. To find the equation that matches this scenario, we need to determine the weekly savings and then express that in an equation form.

Firstly, Michele wants to save an additional $50 ($105 - $55) over the course of 5 weeks (7 weeks - 2 weeks). Dividing $50 by 5 weeks gives us her weekly savings, which is $10 per week.

The equation representing Michele's savings should calculate her total savings, y, after x weeks. Since she starts with $55 and saves $10 each week, the slope (rate of saving per week) is 10, and her starting amount after 2 weeks is $55. This leads us to the equation y - 55 = 10(x - 2), where y is the total amount saved after x weeks.