You're given a hundred dollars and told to spend it all purchasing
exactly a hundred animals at the pet store. Dogs cost $15. Cats cost
a dollar, and mice are 25 cents each.
You have to purchase at least one of each animal.
The question is, how many of each animal do you have to purchase
to equal one hundred animals purchased at exactly one hundred dollars?
Solution to Problem:
3 dogs, 41 cats and 56 mice.Let D stand for the number of dogs, C for the number of cats, and M stand for the number of mice.
Then you can write two equations:
D + C + M = 100 and
15 D + 1 C + 0.25 M = 100.00.
It wasn't going to be five dogs because five dogs would eat up $75 and then you'd only have $25 with which to buy another 95 animals, and it wasn't going to work.
And you know it wasn't zero dogs because that was one of the conditions of the problem.
So, use trial and error with dogs = 4, then 3, 2, and 1 to see which works. The answer turns out to be 3 dogs, 41 cats and 56 mice.
Pet | Number | Total Cost |
---|---|---|
Dogs | 3 | $45.00 |
Cats | 41 | $41.00 |
Mice | 56 | $14.00 |
James Alarie sent in the following Javascript to solve the problem:
for (Dogs=1; Dogs<=6; Dogs++) { for (Cats=1; Cats<=99; Cats++) { for (Mice=1; Mice<=399; Mice++) { Cost=1500*Dogs+100*Cats+25*Mice; if ((Dogs*1+Cats*1+Mice*1 == 100) && (Cost == 10000)) { alert(Dogs+' '+Cats+' '+Mice); }}}}
Correctly solved by:
1. Dave Smith | Toledo, Ohio |
2. William Funk | San Antonio, Texas |
3. Walt Arrison | Philadelphia, Pennsylvania |
4. Jeffrey Gaither | Winchester, Virginia |
5. Peggah Sadeghzadeh | Winchester, Virginia |
6. Richard Johnson | La Jolla, California |
7. Rick Jones | Kennett Square, Pennsylvania |
8. John Funk | Ventura, California |
9. Tina Zahel | Winchester, Virginia |
10. Misty Carlisle | Winchester, Virginia |
11. Jaime Garcia | Winchester, Virginia |
12. John Beasley | Winchester, Virginia |
13. David and Judy Dixon | Bennettsville, South Carolina |
14. Ben Reames | Columbus, Georgia |
15. Pam Hedrick | Winchester, Virginia |
16. James Alarie | University of Michigan -- Flint, Flint, Michigan |
17. George Gaither | Winchester, Virginia |
18. Michael Rodriguez | Great Falls, Montana |
19. Steve Heck | ---------- |