Helping my eldest with mixed fractions and percentage question

[Papa Piccolino]

Hello everyone.

My eldest was set this question for maths - he is in first year high school. I am curious to know how to solve it. It's been more than 30 years since I did this type of work, and I have forgotten most of the concepts.

The question is :
a student sits an exam - of the first 32 questions, he gets 20 correct. Of the remaining questions, he gets 25% correct. The total score he gets for this exam is 40%. Assuming all questions have equal value, what is the total number of questions in the exam ?

I have tried to work this out methodically, but I just can't.

Any help would be very appreciated.

Thank you in advance.

 

[HallsofIvy]

Let "x" be the total number of question. Then the number of "remaining questions", after the first 32, is x- 32. If he got 25% of them right, he got .25(x- 32) of them right. Adding the 20 of the first questions that he got right, he got .25(x- 32)+ 20 questions right. That is, we are told, 40% of all the questions: .25(x- 32)+ 20= .40x.

Alternately, let "x" be the number of "remaining questions". Then there are a total of 32+ x questions. He got 25% of the "remaining questions right so he got .25x of those right. He got 20 of the first 32 right so he got a total of 20+ .25x questions right. If he got 40% of the questions right then 20+ .25x= .40(32+ x). Don't forget to add 32 to whatever value you get for x to find the total number of questions.

 

[Papa Piccolino]

Hello Denis and HallsofIvy.

thanks to both of you for your help.

Boy, I am so out of touch with this stuff. It took me a while to figure out. To think that 30 years ago, I could do this in a few minutes.

Both of your approaches were helpful.

Thanks again.