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 
<pre>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 {{{1:5}}} or {{{1/5}}}, we get: {{{(3x - 2000)/(11x + 1200) = 1/5}}}
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 = {{{11200/4}}}, or 2,800
Therefore, original number of higher-rate tickets sold were: 3(2,800), or {{{highlight_green(8400)}}} 
Also, original number of lower-rate tickets sold were: 11(2,800), or {{{highlight_green(30800)}}}