# Math Help - Percentages stumped me.

1. ## Percentages stumped me.

G'day from Australia. Cody here.
this one stumped me, how may I approach it please?
"a maths exam contained only 2 questions, prob 1 solved by 70%
prob 2 by 60% of students,every pupil solved at least 1 problem.
9 students solved both problems. How many pupils took the exam?
Thank you kindly for any assistance.

2. Originally Posted by cody94
G'day from Australia. Cody here.
this one stumped me, how may I approach it please?
"a maths exam contained only 2 questions, prob 1 solved by 70%
prob 2 by 60% of students,every pupil solved at least 1 problem.
9 students solved both problems. How many pupils took the exam?
Thank you kindly for any assistance.
Let P be the number of pupils that took the exam.

We know that 0.7P pupils got question 1 correct and that 0.6P got question 2 correct. Since 9 students go both problems correct they are counted twice (once for question 1 and again for question 2). So we have overcounted by 9 students. So we get the equation

$0.7P+0.6P-9=P \iff 0.3P=9 \iff P=30$

So the number of pupils that took the exam was 30.

I hope this helps. Good luck.

3. Hello Cody. This is Cody

Since 70% solved problem 1 and 60% solved problem 2 and 9 solved both, then this appears to be a P(A)+P(B)-P(A and B)

Let P(A)=.70 and P(B)=.60

Then A and B=9

So, 9 must be the portion that is the 30 %

9 is 30% of what number?. 9/.30=

4. Thank you very much, Galactus and MTset,
I can see both avenues now.
The "overcounting by 9" was the trick for me.
appreciate you time.
Cody.