Question

Nicole and Milan each opened a savings account today. Nicole opened her account with a starting amount of $240, and she is going to put in $95 per month. Milan opened his account with no starting amount, and he is going to put in $125 per month.

Let x be the number of months after today.


(a)
For each account, write an expression for the amount of money in the account after x months.

Amount of money in Nicole's account (in dollars) =
Amount of money in Milan's account (in dollars) =

(b)
Write an equation to show when the two accounts have the same amount of money.

Answer 1

1)

Nicole:
`95x+240`

Milan:
`125x`

2)

`95x+240=125x`

Explanation:

Question 1)

We know that Nicole opened her account with a starting amount of $240. She also puts in $95 per month.

So, we can write the following expression:

`95x+240`

Where 240 represents the initial deposit of $240 and the 95x represents the $95 for x months.

Milan opened his account with no starting amount, and he's putting in $125 per month.

So, we can write the following expression:

`125x`

Since he didn't put anything at the start, out initial deposit is simply 0. The 125x represents the $125 for x months.

Question 2)

We want to write an equation that shows when the two accounts will have an equivalent balance.

So, we can simply set the two expressions above equal to each other:

`95x+240=125x`

And we're done!

Notes:

Let's solve for x to determine when the two accounts will have the same amount of money. Subtract 95x from both sides:

`240=30x`

Divide both sides by 30:

`x=8`

So, after 8 months, the amount in Nicole's and Milan's account will be equivalent.