Question 485464
Of the final grades received by the students in a certain math course,
1/5 are A ’s, 1/4 are B ’s, 1/2 are C ’s and the remaining 10 grades are D ’s.
 What is the number of students in the course?
:
Let x = total number of students
:
x = {{{1/5}}}x + {{{1/4}}}a + {{{1/2}}}x + 10
Multiply by 20 to clear the denominator
20x = 20*{{{1/5}}}x + 20*{{{1/4}}}a + 20*{{{1/2}}}x + 20(10)
Cancel the denominators and we have
20x = 4x + 5x + 10x + 200
20x = 19x + 200
20x - 19x = 200
x = 200 students
;
You can check the solution, replace x with 200 in the original equation