ratios and numbers

Question

9. The visitors to Walt Disney World in one day were approximately 46 000 and were made up from three types of people: international visitors, interstate visitors and intrastate visitors. The ratio of international visitors to interstate visitors was 3:2 and the ratio of intrastate visitors to interstate visitors was 8:3. How many of each type of person visited Walt Disney World?

Answer 1

Let X = number of interstate visitors  

 

Then if Y = number of international visitors then Y satisfies the ratio  

Y:X :: 3:2  ==>  Y/X = 3/2  ==>  Y = (3/2)X  

 

And if Z = number of intrastate visitors then Z satisfies the ratio  

Z:X :: 8:3  ==>  Z/X = 8/3  ==>  Z = (8/3)X  

 

The total number of visitors was  

 

X + (3/2)X + (8/3)X = 46000

6X + 9X + 16X = 276000

31X = 276000

X ~ 8903 = number of interstate visitors

 

Y = (3/2)X ~ 13354 = number of international visitors  

 

Z = (8/3)X ~ 23742 = number of intrastate visitors  

 

Check:  X + Y + Z = 8903 + 13354 + 23742 = 45999 ~ 46000  

            Y/X = 13354/8903 ~ 1.5 = 3:2 ratio

            Z/X = 23742/8903 ~ 2.6667 = 8:3 ratio