Answer: Van: 10, Bus: 46
Step-by-step explanation:
Let the number of students in each van be represented by v.
Let the number of students in each bus be represented by b.
The question given can be formed into an equation as:
3v + 13b = 628 ...... i
9v + 2b = 182 ......... ii
Multply equation i by 9
Multiply equation ii by 3
27v + 117b = 5652 ........ iii
27v + 6b = 546 ....... iv
Subtract iv from iii
111b = 5106
b = 5106/111
b = 46
Bus = 46
Recall that 9v + 2b = 182
9v + 2(46) = 182
9v + 92 = 182
9v = 182 - 92
9v = 90
v = 90/9
v = 10
Van = 10
There are 4 possible outcomes based on 2 types of wash (deluxe wash & other wash) and 2 vacuum uses (with vacuum and no vacuum). Since customers are equally likely to choose between these, we can run a uniform distribution from 1-4, where each represents one outcome. For example, 1 = deluxe+vacuum, 2=deluxe+no vacuum, 3=other wash+vacuum, 4=other wash+no vacuum. Then after running a large number of simulations (ex. 1000), count the number of the desired result (which is the number 2), and divide by the total number. This will give the probability.