Rounding to the nearest whole percent, the percentage of students who received a merit scholarship but did not receive enough to cover full tuition is approximately 326%.
To find the percentage of students who received a merit scholarship but did not receive enough to cover full tuition, we need to compare the amount they received to the full tuition cost.
Let's denote the minimum scholarship amount as $3,446, and the maximum scholarship amount as $3,473. The cost of full tuition is $4,000.
So, the range of scholarship amounts that did not cover full tuition is from $4,000 (full tuition) to $3,473 (maximum scholarship).
The percentage of students who did not receive enough to cover full tuition is given by the formula)
Percentage=( Number of students with insufficient scholarship/Total number of students with merit scholarship )×100
First, let's find the number of students with insufficient scholarship:
Number of students with insufficient scholarship=Total number of students−Number of students with sufficient scholarship
Number of students with insufficient scholarship=5,348−1,258
Number of students with insufficient scholarship=4,090
Now, plug these values into the formula:
Percentage=(
)×100
Percentage≈325.56%
Rounding to the nearest whole percent, the percentage of students who received a merit scholarship but did not receive enough to cover full tuition is approximately 326%.
Question
Last year’s freshman class at Big State University totaled 5,348 students. Of those, 1,258 received a merit scholarship to help offset tuition costs their freshman year (although the amount varied per student). The amount a student received was N($3,446, $473). If the cost of full tuition was $4,000 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition? (Round your answer to the nearest whole percent.)