Question

One integer is 8​ times another. if the product of the two integers is 128, then find the integers

Answer 1

Let's assign some variable:
x = smaller integer
y = bigger integer

We can set this up as an expression:

`y = 8x`

`xy = 128`

Solve for a variable in the first equation, y is already given, so plug that into the second equation:

`(8x)(x) = 128`

`8x^2=128`

`x^2 = 16`

`x = 4, -4`

Since we only care about the positive values (scalar multiplication), we can rule out the -4, and we are left with x = 4. y is 8 times x, so it has to be 32. Your final answer: x = 4, y = 32