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Question 947879: A cruise called ultimate comfort charges two different rates for seats.
currently ˏ ratio of the number of tickets sold at the higher rate compared to the number of tickets sold at lower rate is 3:11.
however ˏonce the recession beganˏ2000 fewer tickets were sold at the higher rate and 1200 more tickets at the lower rate.
as a result the ratio during the recession was 1 : 5
find the number of each type of ticket sold originally
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let y = number of higher price tickets.
let x = number of lower price ticket.
during normal times the ratio of y/x is equal to 3/11.
solve for x in this equation to get x = (11*y)/3.
once the recession began, the ratio became:
(y-2000) / (x + 1200) = 1/5
solve for y in this equation to get y = 1/5 * (x + 1200) + 2000.
replace x with the value of x you solved for in the first equation to get:
y = 1/5 * ((11y)/3 + 1200) + 2000
multiply both sides of this equation by 5 to get:
5y = (11y)/3 + 1200 + 10000
multiply both side of this equation by 3 to get:
15y = 11y + 3600 + 30000
subtract 11y from both sides of this equation to get:
4y = 33600
divide both sides of this equation by 4 to get:
y = 8400
you have the value of y is equal to 8400
your original ratio was y/x = 3/11
replace y in this ratio to get 8400/x = 3/11
cross multiply to get 3x = 8400 * 11
divide both sides of this equation by 3 to get:
x = (8400 * 11) / 3
solve for x to get x = 30800.
in normal times y = 8400 and x = 30800.
the ratio of y to x is 8400 / 30800 which simplifies to 3/11.
since the recession, the ratio became (y-2000) / (x+1200) = 1/5
replace x with 30800 and y with 8400 in this ratio to get:
(8400 - 2000) / (30800 + 1200) = 1/5.
simplify to get 6400 / 32000 = 1/5.
simplify further to get 1/5 = 1/5.
this confirms that x = 8400 and y = 30800 is the correct number because all the ratios check out ok when using those numbers.
the solution to your problem is:
the number of each type of ticket sold originally is:
higher priced tickets = 8400
lower priced tickets = 30800.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website! A cruise called ultimate comfort charges two different rates for seats.
currently ˏ ratio of the number of tickets sold at the higher rate compared to the number of tickets sold at lower rate is 3:11.
however ˏonce the recession beganˏ2000 fewer tickets were sold at the higher rate and 1200 more tickets at the lower rate.
as a result the ratio during the recession was 1 : 5
find the number of each type of ticket sold originally
Let multiplicative factor for original 3:11 ratio, be x
Then, 3x of the higher rate tickets, and 11x of the lower rate tickets were sold, initially
When the recession began, 2,000 fewer higher-rate tickets were sold, so we get: 3x – 2,000
Also, 1,200 more lower-rate tickets were sold, so we get: 11x + 1,200
With recession ratio being  or  , we get: 
5(3x – 2,000) = 1(11x + 1,200) ------- Cross-multiplying
15x – 10,000 = 11x + 1,200
15x – 11x = 1,200 + 10,000
4x = 11,200
x, or multiplicative factor =  , or 2,800
Therefore, original number of higher-rate tickets sold were: 3(2,800), or 
Also, original number of lower-rate tickets sold were: 11(2,800), or 
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