SOLUTION: You must buy 100 pets and spend $100. You may buy dogs, cats and mice, and you must buy at least one of each pet. Dogs cost $15, cats cost $1 and mice are 25 cents each. How man

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Question 392483: You must buy 100 pets and spend $100. You may buy dogs, cats and mice, and you must buy at least one of each pet. Dogs cost $15, cats cost $1 and mice are 25 cents each. How many of each pet will you buy if you spend exactly $100 and buy exactly 100 pets?
Answer by ankor@dixie-net.com(22740) (Show Source):
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You must buy 100 pets and spend $100. You may buy dogs, cats and mice,
and you must buy at least one of each pet.
Dogs cost $15, cats cost $1 and mice are 25 cents each.
How many of each pet will you buy if you spend exactly $100 and buy exactly 100 pets?
:
Let no. of each animal be, d, c, m
:
Total animal equation
d + c + m = 100
Total cost equation
15d + 1c + .25m = 100
:
We got three unknowns and two equations, but we know the solutions are integers
Eliminate the cats
15d + 1c + .25m = 100
1d + 1c + 1m = 100
---------------------- Subtraction eliminates c
14d - .75m = 0
or
.75m = 14d
m = d
substitute values for d, until you get an integer value for m
when you get to d = 3
m = *3
m =
m = 56 mice
:
We have 3 dogs and 56 mice, then 100 - 59 = 41 cats
:
:
Check that in the cost equation
15(3) + 1(41) .25(56) =
45 + 41 + 14 = 100