Answer :
There are 5 short essay questions on test
Solution:
Let "a" be the number of multiple choice questions
Let "b" be the number of short essay questions
Worth of each multiple choice questions = 3 points
Worth of each short essay questions = 8 points
There are 25 questions in total
number of multiple choice questions + number of short essay questions = 25
a + b = 25
a = 25 - b --------- eqn 1
The test is worth 100 points. Theerefore, we frame a equation as:
number of multiple choice questions x Worth of each multiple choice questions + number of short essay questions x Worth of each short essay questions = 100
[tex]a \times 3 + b \times 8=100[/tex]
3a + 8b = 100 --------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
3(25 - b) + 8b = 100
75 - 3b + 8b = 100
5b = 100 - 75
5b = 25
b = 5
Thus there are 5 short essay questions on test