Final answer:
The math problem involves using given clues to solve for the number of students receiving each letter grade on an exam. Equations are derived from the clues and a system of equations is set up to find the solution. We determine the number of A’s, B’s, C’s, D’s, and F’s through solving these equations.
Step-by-step explanation:
The student's question is a math problem that involves using given clues to determine the number of students who received each grade (A, B, C, D, F) on an exam in Mr. Schuster's class. We are told that there are 32 students in the class, the number of B's and C's together is four times the other grades, one quarter of the students failed, and the fractions of A's and C's are equivalent. To solve this, we set up variables for the number of each grade, use the clues to create equations, and then solve the system of equations.
Let's denote the number of students receiving A's, B's, C's, D's, and F's as a, b, c, d, and f respectively. Here are the clues formatted into equations:
- Total students: a + b + c + d + f = 32
- Four times as many B's and C's: b + c = 4(d + f)
- Quarter failed: f = 32 / 4 (since one quarter failed)
- Equivalent fractions for A's and C's: a/c = 1
From the third clue, f = 8, because 32 divided by 4 is 8. If we also assume that b and c are not zero and that there's at least one A (since a/c = 1), we can set a = c. With these variables, we can solve the system of equations to find the exact number of students with A's, B's, C's, D's, and F's.