Question

Isabel wrote this mystery problem. The quotient is multiple of 6. The dividend is multiple of 9. The divisor is a factor of 12. Write one possible equation to isabel's mystery problem.

Answer 1

Consider the expression
`q=(a)/(b)`. q is called the quotient, a is is the dividend and b is the divisor.

Since q is a multiple of 6, then q has the form
`q=6k` for some integer k.

Since a is a multiple of 9, then a has the form
`a=9s` for some integer s.

Since b is a factor of 12, then if 12 can be expressed of the form
`12=c*b`, for c an integer. Then b has the form
`b=(12)/(m)`

Replacing the preview expression in the initial expression we obtain:

`6k=(9s)/((12)/(m))=(9sm)/(12)\\6*12k=9sm\\72k=9sm\\72k-9sm=0`

Then
`72k-9sm=0,\; for \; k,s,m\in \mathbb{Z}` is a equation to Isabel's problem.