I randomly pick an integer p between 1 and 10 inclusive. What is the probability that I choose a p such that there exists an integer q so that p and q satisfy the equation pq - 4p - 2q = 2? Express your answer as a common fraction.

Guest Jan 11, 2019

#1**+1 **

pq - 4p - 2q = 2

(p - 2)(q -4) = pq -4p - 2q + 8 ......so

pq - 4p - 2q = 2

pq - 4p - 2q + 8 - 8 = 2

(p - 2) (q - 4) - 8 = 2

(p - 2) (q - 4) = 10

When

p = 1, q = -6

p = 3, q = 14

p = 4, q = 9

p = 7, q = 6

So....there are 4 p's that satisfy the equation.....so.....the probability of choosing one of these =

4 / 10 = 2 / 5

CPhill Jan 11, 2019