SOLUTION: A group of more than ten and fewer than thirty people all paid the same amount for a ticket to a concert. If the total cost was 16,490$, how many people are there in the group?

Question 1144216: A group of more than ten and fewer than thirty people all paid the same amount for
a ticket to a concert. If the total cost was 16,490$, how many people are there in
the group?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

Since the group is more than 10 and fewer than 30, we try all the possibilities
from 11 people through 29 people.

We try 11. $16490÷11, we get $1499.09091 That's not a whole number of cents, so
we try 12. $16490÷12, we get $1374.16667 That's not a whole number of cents, so
we try 13. $16490÷13, we get $1268.46154 That's not a whole number of cents, so
we try 14. $16490÷14, we get $1177.85714 That's not a whole number of cents, so
we try 15. $16490÷15, we get $1099.33333 That's not a whole number of cents, so
we try 16. $16490÷16, we get $1030.625 That's not a whole number of cents, so
we try 17. $16490÷17, we get $970 

That's a whole number of cents, so one possibility is 17 people paying $970 each.  

Let's see if there are any other possibilities. So,

we try 18. $16490÷18, we get $916.111111 That's not a whole number of cents, so
we try 19. $16490÷19, we get $867.894737 That's not a whole number of cents, so
we try 20. $16490÷20, we get $824.50

That's a whole number of cents, so another possibility is 20 people paying $824.50 each.  

Let's see if there are any other possibilities. So,

we try 21. $16490÷21, we get $785.238095 That's not a whole number of cents, so
we try 22. $16490÷22, we get $749.545455 That's not a whole number of cents, so
we try 23. $16490÷23, we get $716.956522 That's not a whole number of cents, so
we try 24. $16490÷24, we get $687.083333 That's not a whole number of cents, so
we try 25. $16490÷25, we get $659.60 

That's a whole number of cents, so another possibility is 25 people paying $659.60 each.  

Let's see if there are any other possibilities. So,

we try 26. $16490÷26, we get $634.230769 That's not a whole number of cents, so
we try 27. $16490÷27, we get $610.740741 That's not a whole number of cents, so
we try 28. $16490÷28, we get $588.928571 That's not a whole number of cents, so
we try 29. $16490÷29, we get $568.62069 That's not a whole number of cents, so

That's all the possibilities.  There are three answers:

17 people paying $970 each.
20 people paying $824.50 each.
25 people paying $659.60 each.

Edwin

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