Expert: Steve Holleran - 2/19/2007

Question
there are some rabbits and some rabbit hutches. if seven rabbits are put in each hutch, one rabbits is left over. if nine rabbits are puit in each hutch, one hutch is empty.

Can you Find how many rabbit hutches, and how ,any rabbits there are?

Answer
Hi Crystal,

Okay, lets do this:

H = # of hutches
R = # of rabbits.

"If seven rabbits are put in each hutch, one rabbit is left over"

This gives the equation    7H + 1 = R

"If nine rabbits are put in each hutch, one hutch is empty"

This gives the equation    9(H - 1) = R

Since each equation is = R, they're = to each other:

             7H + 1 = 9(H - 1)

             7H + 1 = 9H - 9

              -2H = -10

                 H = 5.   Then R = 7(5) + 1 = 36.

Check:  7 rabbits per hutch gives 35 + 1 leftover
       9 rabbits per hutch fills 4 hutches and 1 empty.

I hope this helps you out.

Steve Holleran