SOLUTION: You have $100 and you want to spend all of it to buy exactly 100 pets- any combination of hamsters, birds, and fish. Hamsters cost $5 each, brids are $10, and fihes are 50cent each

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Question 427889: You have $100 and you want to spend all of it to buy exactly 100 pets- any combination of hamsters, birds, and fish. Hamsters cost $5 each, brids are $10, and fihes are 50cent each. How many of each kind of pet should you buy?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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You have $100 and you want to spend all of it to buy exactly 100 pets- any combination of hamsters, birds, and fish.
Hamsters cost $5 each, birds are $10, and fishes are 50 cents each.
How many of each kind of pet should you buy?
:
No. of pets equation
h + b + f = 100
:
Cost equation:
5h + 10b + .5f = $100
Multiply the above equation by 2, subtract the 1st equation:
:
10h + 20b + f = 200
h + b + f = 100
------------------------ subtraction eliminates f
9h + 19b = 100
9h = -19b + 100
divide by 9
h = -19%2F9b + 100%2F9
Just looking at this equation, it is apparent there is only one positive integer solution:
b = 1 bird
then
h = -19%2F9(1) + 100%2F9
h = 81%2F9
h = 9 hamsters
then
f = 90 fish
;
:
Check:
5(9) + 10(1) + 90(.5) =
45 + 10 + 45 = $100