Question

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

in the blanks. GUYS PLEASE HELP IM BEEN TRYING THIS 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.
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Answer 1

In 1 week, Ellen and Mariana will each have $576 saved.

Explanation:

Define the variables:

• Let x be the number of weeks.
• Let y be the balance of the account (in dollars).

Ellen's account

If Ellen started by putting $331 in her account and will deposit an additional $245 each week, then:

• 
  `y=331+245x`

Mariana's account

If Mariana made an initial deposit of $325 and will add $251 more each week, then:

• 
  `y=325+251x`

Therefore, the system of equations that represents the problem is:

`\begin{cases}y=331+245x\\y=325+251x\end{cases}`

To calculate how many weeks it will take for Ellen and Mariana to have the same amount saved, substitute the second equation into the first and solve for x:

`\implies 325+251x=331+245x`

`\implies 325+251x-245x=331+245x-245x`

`\implies 325+6x=331`

`\implies 325+6x-325=331-325`

`\implies 6x=6`

`\implies 6x / 6=6 / 6`

`\implies x=1`

Therefore, Ellen and Mariana will each have the same amount saved after 1 week.

To calculate the amount saved after 1 week, substitute x = 1 into one of the equations:

`\implies 325+251(1)=576`

Therefore:

• In 1 week, Ellen and Mariana will each have $576 saved.