SOLUTION: Hotel A and Hotel B Had a total of 6500 guests. After 3/4 of the guests in Hotel a and 3/5 of the guests in hotel B checked out, there were 260 more guests In Hotel B than in hote

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Question 1122087: Hotel A and Hotel B Had a total of 6500 guests. After 3/4 of the guests in Hotel a and 3/5 of the guests in hotel B checked out, there were 260 more guests In Hotel B than in hotel A. How many guests did Hotel A have at first?
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
                  HOTEL A        HOTEL B      

INITIALLY            A             B           TOTAL  6500


AFTER
GUESTS LEFT      %281%2F4%29A          %282%2F5%29B       DIFFERENCE %282%2F5%29B-%281%2F4%29A=260


system%28A%2BB=6500%2C%282%2F5%29B-A%2F4=260%29
Solve this system for A and B.
-
20%282%2F5%29B-%2820%29%28A%2F4%29=20%2A260
8B-5A=5200
8%286500-A%29-5A=5200
52000-8A-5A=5200
-13A=5200-52000
highlight%28A=3600%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let a = no.of guests in Hotel A
let b = no. of guests in Hotel B
:
Write an equation for each statement
:
Hotel A and Hotel B Had a total of 6500 guests.
a + b = 6500
b = (6500-a)
:
After 3/4 of the guests in Hotel a and 3/5 of the guests in hotel B checked out, there were 260 more guests In Hotel B than in hotel A.
That means 2/5 in Hotel B and 1/4 in Hotel A remain
2%2F5b - 1%2F4a = 260
multiply equation by 20, cancel the denominators
4(2b) - 5a = 260 * 20
8b - 5a = 5200
replace b with (6500-a)
8(6500-a) - 5a = 5200
52000 - 8a - 5a = 5200
-13a = 5200 - 52000
-13a = -46800
a = %28-46800%29%2F%28-13%29
a = 3600 guests originally in Hotel A
:
;
Check; find the no. guests in B: 6500 - 2600 = 2900, (1/4) of 3600 = 900
2%2F5*2900 = 1160
1160 - 900 = 260