Math Help?

Question

Ok here is the challenge...
You have $100 and must buy 100 raffle prizes. You decide on the following three types of prizes.

Play tickets whcih are $15 each
Rubber ducks which are $1 each
Pencils which are $.25 each
You mist purchase at least 1 of each prize.
How many of each prize do you habe to spend exactly $100 and to get exactly 100 prizes.

Show work please ... thanks

Thanks dragon fly... I will choose you best... youre great!!!

Answer 1

I am not sure how to show the work but..... here is what I did.....
You will always have to buy 4 pencils at a time Four for a dollar....

I started out with 2 tickets (for $30.00) and I added 40 pencils (for $10.00) That gave me 42 prizes with $40 spent... I need to get the same amount of money and prizes between the pencils and the tickets.... So I added another ticket to my stuff...... that gave me 43 prizes with $55 spent. I added four more sets of pencils (16 total) That gave me 59 total prizes with $59 spent..... Since the ducks are a dollar apiece I subtracted 100 from 59 to get 41 Ducks....

So you end up with ::
3 Tickets $45.00

56 Pencils $14.00

41 Ducks $41.00

Total 100 Prizes $100.00

I know you want to show your work, and I am sure there is a formula, but I don't know what it is...I just used the trial and error process.... Sorry!