<PRE><B>Question 1122087</B>
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
{{{2/5}}}b - {{{1/4}}}a = 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 = {{{(-46800)/(-13)}}}
a = 3600 guests originally in Hotel A
:
;
Check; find the no. guests in B: 6500 - 2600 = 2900, (1/4) of 3600 = 900
{{{2/5}}}*2900 = 1160
1160 - 900 = 260



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