SOLUTION: a maths exam contained two problems. Problem A was solved by 70% of the students. Problem B was solved by 60%. Every students solved at least one of the problems. Nine students sol
Question 9410: a maths exam contained two problems. Problem A was solved by 70% of the students. Problem B was solved by 60%. Every students solved at least one of the problems. Nine students solved both problems. how many students sat the exam? Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website! Let x = number of students who took the exam.
.7 x = number of students who solved Problem A.
.6 x = number of students who solved Problem B.
9 = number of students who solved both problems correctly.
Since everyone got at least one problem correct, adding the two categories of students (.7x + .6x) together would include ALL the students who took the exam, but the 9 students who got both problems correct will be counted twice. So when writing the equation, you add these two categories and subtract the overlap, in order to get the total number of students who took the exam
This gives the following equation:
.7x + .6x - 9 = x
1.3 x - 9 = x
Subtract x from each side
1.3x - x - 9 = x - x
.3x - 9 = 0
.3x = 9
Divide by .3
x = = = 30
Check:
70% of 30 = 21
60% of 30 = 18
The total of these is 39, which means that 9 got both problems correct.
