Question

If x and y are positive integers less than 20 for which x⋅y⋅xy=76, what is the value of x⋅y?

a) 1
b) 2
c) 4
d) 8

Answer 1

After factoring the equation x*y*xy = 76 and checking possible factor pairs of 76, we find that (x, y) = (2, 2) satisfies the condition. Thus, the value of x⋅y is 4.

Step-by-step explanation:

To solve for the value of x⋅y given that x and y are positive integers less than 20 and x⋅y⋅xy = 76, we can factor the equation as follows:

• x⋅y⋅xy = x²y² = 76
• Since 76 is not a perfect square, and the only factors of 76 less than 20 are 1, 2, 4, and 19, we start by trying these.
• Checking the factor pairs, we find that (x, y) = (2, 2) satisfies the condition, as 2⋅2⋅2⋅2 = 2²2²2 = 16, and 16 < 76.
• Since (x, y) = (2, 2) works, the value of x⋅y is 2⋅2 = 4.

Therefore, the value of x⋅y is 4.