Question

At the beginning of the year, Gabriel had 25 in savings and saved an additional14 each week thereafter. Adrian started the year with 80 and saved9 every week. Let gg represent the amount of money Gabriel has saved tt weeks after the beginning of the year and let aa represent the amount of money Adrian has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t, comma, and determine the number of weeks after the beginning of the year until Gabriel and Adrian have the same amount of money saved.

Answer 1

To write an equation for each situation, Gabriel's savings after t weeks would be gg = 25 + 14t, and Adrian's savings after t weeks would be aa = 80 + 9t. The number of weeks until they have the same amount can be found by setting gg equal to aa and solving for t.

Step-by-step explanation:

To write an equation for each situation, we need to first determine the amount of money Gabriel and Adrian will have saved after a certain number of weeks. Let's represent the amount of money saved by Gabriel after t weeks as gg and the amount saved by Adrian as aa.

For Gabriel, we know that at the beginning of the year he had $25 and saved an additional $14 each week. So the equation for Gabriel's savings after t weeks would be gg = 25 + 14t.

Similarly, for Adrian, we know that he had $80 at the beginning of the year and saved $9 each week. So the equation for Adrian's savings after t weeks would be aa = 80 + 9t.

To determine the number of weeks after the beginning of the year until Gabriel and Adrian have the same amount of money saved, we need to set gg and aa equal to each other and solve for t.