The Correct Answer and Explanation is:
The correct answer is 11.
To find the highest number of credits Adrian can take, we must create an inequality that represents his total expenses being less than or equal to his total scholarship funds. Adrian’s scholarship provides him with a maximum of $16,500 for the academic year.
First, we identify all his costs. The main variable cost is tuition, which is priced at $1,250 per credit hour. We can represent the unknown number of credits with the variable ‘c’, making the total tuition cost 1250c.
Next, we calculate the fixed costs. Adrian has a student services fee of $350 per semester. Over a full academic year, which consists of two semesters (fall and spring), this fee amounts to 2 times $350, for a total of $700. Additionally, he plans to spend a flat amount of $1,100 on textbooks for the entire year.
We can now combine these expenses into one inequality. The sum of the tuition, fees, and textbook costs must not be more than his $16,500 scholarship. This gives us the following mathematical statement:
1250c + 700 + 1100 ≤ 16500
To solve for ‘c’, we begin by simplifying the inequality. We combine the constant terms for fees and textbooks:
1250c + 1800 ≤ 16500
Then, we isolate the term containing the variable ‘c’ by subtracting 1800 from both sides of the inequality:
1250c ≤ 14700
Finally, we divide both sides by 1250 to determine the value of ‘c’:
c ≤ 11.76
The result, 11.76, represents the absolute maximum number of credits the funds can cover. However, since a student can only register for a whole number of credits, Adrian cannot take 11.76 credits. To stay within his budget, he must round down to the nearest whole number. Therefore, the highest number of credits Adrian can afford is 11.
