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, 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 = {{{-19/9}}}b + {{{100/9}}}
Just looking at this equation, it is apparent there is only one positive integer solution:
b = 1 bird
then
h = {{{-19/9}}}(1) + {{{100/9}}}
h = {{{81/9}}}
h = 9 hamsters
then 
f = 90 fish
;
:
Check:
5(9) + 10(1) + 90(.5) =
45 + 10 + 45 = $100