To determine the minimum amount Laura should expect to contribute to her college education for all four years, let's break down the costs and contributions step-by-step.
### Step 1: Calculate the Total Estimated Cost per Year
We start by summing up the costs per year for tuition, room and board, books, and lab and facilities fees.
- Tuition: [tex]$29,500
- Room and Board: $[/tex]9,600
- Books: [tex]$2,125
- Lab and Facilities Fees: $[/tex]850
Total estimated cost per year:
[tex]\[ 29,500 + 9,600 + 2,125 + 850 = \$42,075 \][/tex]
### Step 2: Calculate the Grant and Scholarship Contributions
Laura receives a grant that covers 30% of her annual tuition and a scholarship that covers the full cost of her books.
- 30% of Tuition:
[tex]\[ 0.30 \times 29,500 = \$8,850 \][/tex]
- Book Scholarship:
[tex]\[ \$2,125 \][/tex]
### Step 3: Calculate the Remaining Costs Laura Has to Cover Annually
Subtract the contributions from the grant and scholarship from the total estimated costs.
- Remaining Tuition (after Grant):
[tex]\[ 29,500 - 8,850 = \$20,650 \][/tex]
- Remaining Cost per Year (excluding books covered by scholarship):
[tex]\[ 20,650 + 9,600 + 850 = \$31,100 \][/tex]
### Step 4: Calculate the Total Remaining Costs over Four Years
We calculate the total cost Laura has to cover over the entire four years.
- Annual Remaining Costs (excluding books, would be consistent each year):
[tex]\[ \$31,100 \][/tex]
- Total Remaining Costs over Four Years:
[tex]\[ 31,100 \times 4 = \$124,400 \][/tex]
### Step 5: Find Out Which Minimum Contribution Corresponds to the Given Choices
From the calculated total remaining cost over four years, we need to choose from the given options.
- Choices are:
- [tex]$111,860
- $[/tex]117,810
- [tex]$124,400
- $[/tex]132,900
The total amount Laura should expect to contribute to her college education over four years is [tex]$124,400. Therefore, the correct answer is:
\[ \boxed{\$[/tex]124,400} \]
