Question

Jessica currently has $180 dollars in her bank account and will add an additional $15 each week. Nate has $120dollars in his account and will add $20 each week.A. After how many weeks will they have the same amount of money in their accounts?B. What is the amount, in dollars, that each person will have after this many weeks?

Answer 1

(a)12 weeks

(b)$360

Step-by-step explanation:

Part A

Let the number of weeks when they have the same amount of money in their accounts be x.

`\begin{gathered} \text{Jessica's amount after x weeks }=180+15x \\ \text{Nate's amount after x weeks }=120+20x \end{gathered}`

If the amount of money is equal:

`180+15x=120+20x`

Solve for x:

`\begin{gathered} 180-120=20x-15x \\ 60=5x \\ (60)/(5)=(5x)/(5) \\ x=12 \end{gathered}`

Therefore, they will have the same amount of money after 12 weeks.

Part B

The amount that each person will have, (Using Jessica's Equation)

`\begin{gathered} \text{Amount}=180+15x \\ =180+15(12) \\ =180+180 \\ =\$360 \end{gathered}`

The amount, in dollars, that each person will have after 12 weeks is $360.