Answer:
8 correct, 6 wrong : 14 problems tried!
Explanation:
If she gets 8 points by every question correctly answered and she got 13 points in total, she must have answered at least two questions (if she answers only 1 she gets at maximum 8 points, not reaching 13 never).
So lets try to find the solution.
If she answered 2 and mistaken 1 she would get:
2*8 - 1*5 = 16 - 5 = 11 -> So this is not correct.
If she answered 3 correct she would get 24 points, with 2 mistaken answers she would have:
8*3 - 5*2 = 24 -10 = 14
We need to see something important in this patterns:
As the wrong questions always subtract a multiple of 5, and we need a result of 13, we CAN'T have an even number of wrong questions, because this would imply a subtract of numbers like 10, 20, 30, etc; and as the correct answers only give us even numbers (8, 16, 32, 64, etc), the result of subtracting 2 even numbers would never be 13. And as we will be subtracting a number with a 5 in the units, the points for correct answers MUST have an 8 in the units, as 8-5=13.
So, lets go to the first posible number that ends in 8 and is multiple of 8 and greater than 16. This is 48. 48 = 6*8, this is, lets think about 6 correct answers that sum 48 points.
We now need to subtract a number to 48 that gives us 13. Which is?
48 - x = 13 <----> x = 35
So, we need a number of incorrect answers that sum 35. As every wrong answer sums 5 points, we need 7 wring answers (7*5 = 35):
8*6 - 5*7 = 48 - 35 = 13 points!!
There were 14 problems tried to solve