Question

A pupil gets 15 points for correct answer and -34 for wrong one. The pupil had solved no more than 150 problems, he got 114 points. How many problems did he solve right and how many wrong?

Answer 1

have you tried to form any equations or inequations..?

Answer 2

but what I'd suggest is let x = correct answers and y = incorrect answers

so x + y = 150

now look at the points

15x - 34y = 114

now solve the 2 equations simultaneously

Answer 3

you could set the number of questions equation as an inequation

\[x + y \le 150\]

Answer 4

This is a pair of simultanous equations.

Let x be the number of correct questions he answers and y be the number of wrong questions he answers.

You can write up two equations by answering these:
1) How many questions did he answer altogether, and express this in terms of x and y.
2) How many total correct points does he get if he answers x questions correct?
3) How many total incorrect points does he get if he answers y questions wrong?
4) How many pts in total for 2) and 3) combined?

Then the equations formed by 1) and 4) can be solved simultaneously.

Answer 5

a you could graph the inequation and equation, find the point of intersection

Answer 6

But how would I get an integer solution? I seem to get fractions, but it would be quite weird, if he had answered half of a question right...

Answer 7

@Zyberg did you solve it?
i think i have a solution...

Answer 8

@baru I didn't, could you tell me the solution?

Answer 9

62 right and 24 wrong...
but its a bit of a brute force solution...
as in, if we are given different set of numbers for the same problem.. the solution won't work

Answer 10

he only way we can get 114 (with last digit 4) for the final score is if

the number of correct answrs (x) is even (thus ending with the digit 0)

and the number of incorrect answers (y) a number with the last digit 4
(so that 34 * number ending with 4 = number ending with 6)

Answer 11

That is some very good observation! Thank you for taking your time!

Answer 12

now to get an idea of the range of numbers we are working with, i solved
\[15x-34y=0\\x+y=0\]

we get roughly x=105 and y=45 (x: no of correct answers y:no of wrong ans)

Answer 13

this means that if the number of wrong answers HAS to be less than 45,
because if it was more, then the total score would end up being negative

Answer 14

so the possibilites for y are
4
14
24
34
44

Answer 15

the corresponding number of points lost amount to
4*34=136
14*34=476
24*34=816
....

Answer 16

then we add each of the above numbers to 114 , and check which one is divisible by 15

Answer 17

turns out 114+816=930
which is divisible by 15

Answer 18

816/34 = 24 (wrong answers)
930/15=62 (right answers)