# Thread: Ratio Word Problem Help!!

1. ## Ratio Word Problem Help!!

The ratio of rooms in a hotel that are occupied to unoccupied are in the
ratio 6:5. The next morning, people check out of 230 of the rooms. Nobody
checks in. The ratio of occupied rooms to unoccupied rooms is now 4:5. Use
this information to figure out how many rooms there are in the hotel in all.

2. Originally Posted by casey_k
The ratio of rooms in a hotel that are occupied to unoccupied are in the
ratio 6:5. The next morning, people check out of 230 of the rooms. Nobody
checks in. The ratio of occupied rooms to unoccupied rooms is now 4:5. Use
this information to figure out how many rooms there are in the hotel in all.
$\displaystyle v$ = number occupied

$\displaystyle u$ = number unoccupied

$\displaystyle \frac{v}{u} = \frac{6}{5}$

$\displaystyle 5v = 6u$

$\displaystyle \frac{v-230}{u+230} = \frac{4}{5}$

$\displaystyle 5v-1150 = 4u+920$

$\displaystyle 6u-1150 = 4u+920$

$\displaystyle 2u = 2070$

$\displaystyle u = 1035$

finish up and find $\displaystyle v$

3. Thank you!
I got 2277 for the answer