In certain contest show, Pepita Cacahuate was asked 30 questions.

Question

In certain contest show, Pepita Cacahuate was asked 30 questions. She got 8 point per right answer she gave, she lost 5
points per wrong answer she gave, and she got no points for those unanswered questions. There are two ways in which she could have 13 points. If a and b designate the number of unanswered questions for the first and the second option respectively, then find the sum a+b.

Answer 1

Hi,

8x -5y= 13

The next step is to set up a table of values. The x and y values need to be whole numbers and x+y ≤30.

 

Another method to come up with the two numbers is to graph the linear equation, y= (8/5)x -13/5, locate the two integral coordinates.

(x,y)

(6,7)               6 + 7 + a = 30         a= 17

(11, 15)         11 + 15 + b= 30      b=4

Therefore, 

a + b= 17 + 4

= 21