Problem solving

Question

During a fete, there was a game show called "The big 20". A contestant is paid $5 for each correct answer, but must pay back $4 for each wrong answer. After answering 20 questions on the show, John won $55. How many questions did he answer correctly?

Answer 1

let no. of correct answers=x, no. of incorrect answers=y.

x+y=20.....(1)

5x-4y=55 ......(2)

from equation(1)   5x+5y=100   (subtracting this to equation (2))

-9y=-45

y=5

so, x=15

so no. of correct answers=15.