Question

Which situation can be represented by this equation?

2,500 + 40x = 7,300 - 60x

A) Jay started with 2,500 blankets for the blanket drive. He collects 40 more blankets each week. Candace started with 7,300 blankets for the blanket drive, and she collects 60 more blankets each week. What is x, the number of weeks that need to pass in order for Jay and Candace to have the same number of blankets?

B) Jay started with savings of 2,500 and adds 40 to his savings each week. Candace started with 7,300 in savings and spends 60 of her saving each week. What is x, the number of weeks that need to pass in order for Jay and Candace to have the same amount of savings?

C) Jay earns 2,500 points on his rewards card each time he reaches a new customer level. Candace earns 7,300 points on her rewards card each time she reaches a new customer level. What is x, the number of levels that Jay and Candace would have to achieve to have an equal number of points?

D) Jay has a cylindrical fish tank that originally contained 2,500 fl oz of water and is being filled at a rate of 60 fl oz per minute. Candace has a cylindrical fish tank that originally contained 7,500 fl oz of water and is being drained at a rate of 40 fl oz per minute. What is x, the number of minutes that needs to pass so that Candace's fish tank will contain more water than Jay's fish tank?

Answer 1

The equation 2,500 + 40x = 7,300 - 60x does not have a solution in the context of the given situations.

Step-by-step explanation:

The equation 2,500 + 40x = 7,300 - 60x can be represented by situation A) Jay starting with 2,500 blankets for the blanket drive and collecting 40 more blankets each week, while Candace starts with 7,300 blankets and collects 60 more blankets each week. We need to find x, the number of weeks for Jay and Candace to have the same number of blankets.

In this situation, the equation represents the total number of blankets for Jay (2,500 + 40x) being equal to the total number of blankets for Candace (7,300 - 60x). We can solve this equation by combining like terms and isolating x:

2,500 + 40x = 7,300 - 60x
-100x = 4,800
x = -48

Since the solution is negative, it does not make sense in the context of the problem. Therefore, this situation does not have a solution.