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

Answer:

Consider the expression $q=\frac{a}{b}$. 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 $b=\frac{12}{m}$

Replacing the preview expression in the initial expression we obtain:

$6k=\frac{9s}{\frac{12}{m}}=\frac{9sm}{12}\\6*12k=9sm\\72k=9sm\\72k-9sm=0$

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