Question

Andre and Elena are each saving money, Andre starts with 100 dollars in his savings account and adds 5 dollars per week, Elena starts with 10 dollars in her savings account and adds 20 dollars each week.After 4 weeks who has more money in their savings account?? Explain how you know.After how many weeks will Elena and Andre have the same amount of money in their savings account? How do you know?

Answer 1

We can model each savings account balance in function of time as a linear function.

Andre starts with $100 and he adds $5 per week. If t is the number of weeks, we can write this as:

`A(t)=100+5\cdot t`

In the same way, as Elena starts with $10 and saves $20 each week, we can write her balance as:

`E(t)=10+20\cdot t`

We can evaluate their savings after 4 weeks (t=4) as:

`\begin{gathered} A(4)=100+5\cdot4=100+20=120 \\ E(4)=10+20\cdot4=10+80=90 \end{gathered}`

After 4 weeks, Andre will have $120 and Elena will have $90.

We can calculate at which week their savings will be the same by writing A(t)=E(t) and calculating for t:

`\begin{gathered} A(t)=E(t) \\ 100+5t=10+20t \\ 5t-20t=10-100 \\ -15t=-90 \\ t=(-90)/(-15) \\ t=6 \end{gathered}`

In 6 weeks, their savings will be the same. We know it beca