To determine which statement about the yearly costs is true, let's carefully analyze both options A and B step-by-step:
### Option A:
1. Costs:
- Tuition & Fees: \[tex]$28,000
- Room & Board: \$[/tex]10,000
- Total Costs: \[tex]$28,000 + \$[/tex]10,000 = \[tex]$38,000
2. Financial Aid:
- Scholarships & Grants: \$[/tex]18,000
- Work-Study: \[tex]$7,000
- Total Financial Aid: \$[/tex]18,000 + \[tex]$7,000 = \$[/tex]25,000
3. Out-of-Pocket Cost:
- Out-of-Pocket = Total Costs - Total Financial Aid
- Out-of-Pocket = \[tex]$38,000 - \$[/tex]25,000 = \[tex]$13,000
### Option B:
1. Costs:
- Tuition & Fees: \$[/tex]28,000
- Room & Board: \[tex]$9,000
- Total Costs: \$[/tex]28,000 + \[tex]$9,000 = \$[/tex]37,000
2. Financial Aid:
- Scholarships & Grants: \[tex]$18,000
- Work-Study: \$[/tex]4,000
- Total Financial Aid: \[tex]$18,000 + \$[/tex]4,000 = \[tex]$22,000
3. Out-of-Pocket Cost:
- Out-of-Pocket = Total Costs - Total Financial Aid
- Out-of-Pocket = \$[/tex]37,000 - \[tex]$22,000 = \$[/tex]15,000
### Savings Comparison:
To determine which option saves more, compare the out-of-pocket costs:
- Savings from Option A compared to Option B:
- A Saves = \[tex]$15,000 (Option B Out-of-Pocket) - \$[/tex]13,000 (Option A Out-of-Pocket) = \[tex]$2,000
- Savings from Option B compared to Option A:
- B Saves = \$[/tex]13,000 (Option A Out-of-Pocket) - \[tex]$15,000 (Option B Out-of-Pocket) = -\$[/tex]2,000
Since negative savings indicate additional expenses rather than savings, let's look at the provided statements again:
- Option A will save her \[tex]$4,500. (Incorrect, Option A saves \$[/tex]2,000)
- Option B will save her \[tex]$7,000. (Incorrect, Option B results in an additional expense of \$[/tex]2,000)
- Option B will save her \[tex]$11,000. (Incorrect, Option B results in an additional expense of \$[/tex]2,000)
- Option A will save her \[tex]$15,500. (Incorrect, Option A saves \$[/tex]2,000)
None of the provided statements are accurate with respect to the given numerical results. The correct saving here, based on the calculations, is that Option A will save her \$2,000 compared to Option B.
