A maths exam contained 2 problems...?

Question

Problem A was solved by 70% of the students.

Problem B was solved by 60 % every student solved at least one of the problems. 9 students solved both problems.

How many students did the exam??

thanksss =D

x*x

Answer 1

Let N be the number of students doing the exam.

Let a be the number of students solving the problem A

Let b be the number of students solving the problem B

Then 0.7 N = a and 0.6 N = b

Thus 1.3 N = a + b

Now, there are 9 students solved both problems and each student solve at least one of the problem. Hence, the number of students doing the exam is equal to a + b - 9

Thus, N = a + b - 9

i.e.,   N = 1.3 N - 9

It follows that N = 10/3 * 9 = 30

Answer 2

Hope this makes sense to you.

Let x = total number of students who took the exam.

Let y = number of students who did problem A

Let z = number of students who did problem B

x = y + z - 9 (because 9 students did both problems, so there is an overlap in y and z)

Rearrange equation for x:

x = y + z - 9

x + 9 = y + z

.7x = y (70% of total students = number of students who did A)

.6x = z (60% of total students = number of students who did B)

Add these two equations together to get:

1.3x = y + z

Set the two equations equal to eachother (y + z = y + z):

x + 9 = 1.3x

Solve for x:

9 = .3x

x = 30

30 students did the exam.

Let's check:

Problem A:

y = .7x = .7(30) = 21

Problem B:

z = .6x = .6(30) = 18

y + z = 21 + 18 = 39

y + z = x + 9 = 30 + 9 = 39

IT WORKS!

Answer 3

100-70-60=30% solve both.

30% is 9 students

hence 100% is 9*100/30=30 students.