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.

R^2 at SCC

RELATED QUESTIONS
A math test has two problems. The first was solved by 70% of the students. The second was (answered by tvandenberg)

In an exam, two reasoning problems, 1 and 2, are asked. 35% students solved problem 1... (answered by ikleyn)

Henry solved a certain number of algebra problems in an hour, but his older brother... (answered by Boreal)

Please help me on this problem. I will write it how it looks in my text book.The two jugs (answered by Paul,Earlsdon,stanbon)

Hi I have a couple of problems that I would like to know how to solve. The involve the... (answered by checkley71)

In the first week students at a school solved 25 percent of their monthly quota of... (answered by Theo)

problem of maths is given to three students whose chances of solving it are... (answered by Theo)

John and Anita can solve 90% and 70% respectively of statistics problems. If they (answered by stanbon)

a total of 50 juniors and seniors were given a mathmatics test. the 35 juniors attained... (answered by rfer)