Question

The product of two integers is about 50 less than one of the integers. Explain your answer. Think of three or more possible pairs of integers.

Answer 1

An integer is a whole number and the product of numbers means to multiply them. So so we know that:
x * y = x - 50

So the product (x * y) is 50 less than one of the integers ( x - 50)

I can divide both sides by x:
y = (x - 50) / x where x is not zero
y = x/x - 50/x
y = 1 - 50/ x

x can no longer be zero since you cannot divide by zero

the only way for y to be a whole number is if 50/x is a whole number. 50/x can onky be a whole number if x is a factor of 50. so take any factor of 50 and that will be possible answers.
factors of 50: 1,2,5,10,25,50

these would be possible x values. To to find corresponding y values plug in x
y = 1 - 50/1
y = 1 - 50
y = -49
So first pair is (1, -49)
do the same for the rest and get
(2, -24)
(5, -9)
(10, -4)
(25, -1)
(50, 0)