Question 947879
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.