Question

You begin with $90 in your savings account and your friend begins

with $35 in her savings account. You deposit $10 in savings each
week, and your friend deposits $15 in savings each week.
a. Write and graph a system of linear equations that
represent the amounts in each of your savings
accounts
b. Your friend says that in 10 weeks you will both
have the same amount of money in your savings
accounts. Is your friend correct? Use the graph
from part (a) to explain your answer.

Answer 1

F(f) = 15t + 35 represents the total amount of savings your friend would make in t weeks.

F(d) = 10t + 90 represents the total amount of saving you, darian, would make in t weeks.

When you graph the equations, plugging in different values for t, you can see that the graphs intersect at (11,200). This means that at 11 weeks, both you and your friend have the same amount of money saved up, $200. They will not have the same amount of money in 10 weeks.

Answer 2

a.
`y=10x+90`

`y=15x+35`

b. Your friend is wrong.

Explanation:

If you begin with $90 and add $10 each week, then we express it as

`y=10x+90`

Where
`x` refers to weeks and
`y` refers to the total amount of money in you savings account.

On the other hand, your friend begins with $35 and deposits $15 each week, the equation that expresses your friend's savings is

`y=15x+35`

Therefore, the sytem of linear equation that models this situation is

`y=10x+90`

`y=15x+35`

The graph attached shows this system. There you can notice that the solution is (11, 200), which means in 11 weeks both will have the same amount saved.

Therefore, your friend is wrong, because after 10 weeks you won't have the same amount.