To determine how much Caleb and his family need to save each month, let's break down their expenses and savings over the four-year period step by step.
### Step 1: Calculate the Total Cost
First, we need to figure out the total cost Caleb will face in his first year of college. The category for room and board is not considered because Caleb will be living at home, making that cost [tex]$0.
Given costs are:
- Tuition: \$[/tex]9,350
- Room and board: \[tex]$0
- Books and fees: \$[/tex]1,650
- Transportation: \[tex]$2,140
- Other: \$[/tex]1,110
The total cost [tex]\( T \)[/tex] is:
[tex]\[ T = \text{tuition} + \text{room and board} + \text{books and fees} + \text{transportation} + \text{other} \][/tex]
[tex]\[ T = 9350 + 0 + 1650 + 2140 + 1110 = 14250 \][/tex]
### Step 2: Subtract the Grants
Caleb expects to receive \[tex]$4,500 in grants. Therefore, the net amount \( N \) that Caleb needs to save is the total cost minus the grants:
\[ N = T - \text{grants} \]
\[ N = 14250 - 4500 = 9750 \]
### Step 3: Calculate the Total Number of Months for Savings
Caleb has a total of 4 years to save. Since there are 12 months in a year, the total number of months \( M \) is:
\[ M = 4 \times 12 = 48 \]
### Step 4: Calculate the Monthly Savings Amount
Finally, to find out the minimum amount Caleb needs to save each month \( S \), we divide the net amount needed by the total number of months:
\[ S = \frac{N}{M} = \frac{9750}{48} = 203.125 \]
### Conclusion
Thus, Caleb and his family should save at least \$[/tex]203.125 each month. Since \[tex]$203.125 is closest to \$[/tex]200 among the provided options, the best approximation is:
[tex]\[ \boxed{\$200} \][/tex]
Therefore, Caleb and his family should save at least \$200 each month to ensure they have enough money for his first year of college.
