a class of ten students took a math exam. each problem was solved by exactly seven of the ten students the first nine students in the class solved exactly four problems each . what is the number of problems solved by the tenth student
If there were x problems, then
9*4 + x = 7x
Well, it looks like the tenth student must be quite the overachiever! Since each problem was solved by exactly seven of the ten students, and the first nine students solved exactly four problems each, we can calculate the total number of problems solved by the first nine students:
9 students × 4 problems each = 36 problems
Now, since there were 10 students in total, the remaining four problems must have been solved by the tenth student:
Total problems - Problems solved by the first nine students = Problems solved by the tenth student
(36 problems) - (36 problems) = 0 problems
So, according to my calculations, the tenth student didn't solve any problems. Perhaps they were just there for moral support!
To find the number of problems solved by the tenth student, we can use the information that each problem was solved by exactly seven out of ten students and the first nine students solved exactly four problems each.
Let's calculate the total number of problems solved by the first nine students. Since each of them solved four problems, the total number of problems is 9 students * 4 problems/student = 36 problems.
Now, we know that each problem was solved by exactly seven students. Therefore, the total number of problems solved by all ten students is 7 students/problem * number of problems = 10 students * number of problems.
Setting up the equation, we have 7 * number of problems = 36 problems.
To solve for the number of problems, we can divide both sides of the equation by 7:
(number of problems) = 36 problems / 7 = 5.142857142857143
Since the number of problems cannot be a fraction or decimal for this question, it means that the tenth student did not solve any problems.
To find the number of problems solved by the tenth student, we first need to calculate the total number of problems solved by the first nine students.
Since each student solved exactly four problems, the total number of problems solved by the first nine students is 9 students × 4 problems = 36 problems.
We also know that each problem was solved by exactly seven out of the ten students. Therefore, the total number of times a problem was solved is 10 students × 7 problems = 70.
To find the number of problems solved by the tenth student, we need to subtract the total number of problems solved by the first nine students from the total number of times a problem was solved.
Number of problems solved by the tenth student = Total number of times a problem was solved - Total number of problems solved by the first nine students
Number of problems solved by the tenth student = 70 - 36
Therefore, the tenth student solved 34 problems.