Question

Write a system of equations to describe the situation below, solve using substitution, and fill

in the blanks. GUYS PLEASE IVE BEEN TRYING TO FIGURE THIS OUT FOR SO LONG.

Ellen and Mariana each opened a savings account on the same day. Ellen started by putting
$331 in her account, and she will deposit an additional $245 each week. Mariana made an
initial deposit of $325, and she will add $251 more each week. Eventually, Ellen and Mariana
will each have the same amount saved.
How many weeks will that take? What is that amount?


In ___ weeks, Ellen and Mariana will each have $___ saved.

Answer 1

2 weeks, $576

Explanation:

Let's create a function for each person's savings account.

Ellen: Because she starts out with 331 and adds an additional 245 each week, we can write the equation

b=331+(245w-245) (b being the balance, and w being the week number, assuming that the first deposit started on week 1)

Mariana: We can do the same thing here but with different numbers

b=325+(251w-251) (using the same rules as Ellen's equation)

Since we're solving for when each balances are equal to each other, we can set the functions equal to each other as well.

331+(245w-245)=325+(251w-251)

Now all we have to do is solve for w.

Simplifying the equations:
86+245w=74+251w

Isolating w:
12=6w

Solving for w:
2=w

Meaning that their balances will be the same after 2 weeks.
When we plug w into either of the equations, we get $576.