Question

The product of two integers is about 50 less than one of the integers. Think of 3 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)

I can't take credit for this. SamuelS gave this answer