Let's break down the problem step by step to determine the reasonable estimate of the monthly amount Carly needs to deposit into her savings account over the next 3 years.
### Step 1: Total Amount Needed
Carly needs [tex]$\$[/tex]12,000[tex]$ for her first year of college.
### Step 2: Current Savings
She already has $[/tex]\[tex]$2,900$[/tex] in her savings account.
### Step 3: Remaining Amount to Save
To find out how much more Carly needs to save, subtract her current savings from the total amount needed:
[tex]\[
12,000 - 2,900 = 9,100
\][/tex]
Carly needs to save an additional [tex]$\$[/tex]9,100[tex]$.
### Step 4: Time Frame
Carly has 3 years to save this amount.
### Step 5: Number of Months in 3 Years
There are 12 months in a year, thus:
\[
3 \text{ years} \times 12 \text{ months/year} = 36 \text{ months}
\]
### Step 6: Monthly Savings Requirement
Now, we need to find out how much Carly needs to save each month. Divide the remaining amount needed by the number of months:
\[
\frac{9,100}{36} \approx 252.78
\]
So, Carly needs to save approximately $[/tex]\[tex]$252.78$[/tex] per month.
### Conclusion:
We compare this amount to the given options: [tex]$\$[/tex]150, \[tex]$250, \$[/tex]350[tex]$, and $[/tex]\[tex]$450$[/tex]. The closest estimate is [tex]$\$[/tex]250[tex]$.
Therefore, Carly needs to deposit approximately $[/tex]\[tex]$250$[/tex] per month into her savings account over the next 3 years to be able to pay for her first year of college.
