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

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): You can put this solution on YOUR website!
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

RELATED QUESTIONS
Hi I am a mother of a pre-algebra student and I am having a problem helping her with this (answered by askmemath)

You have $100 dollars. You must purchase a total of 100 animals. Dogs costs $10 each.... (answered by ankor@dixie-net.com)

If you spend $100 on 100animals (8hens=$1, 1sheep=$1 and cows cost $10) and you must buy... (answered by josmiceli)

You have to buy 100 animals with $100.00. Dogs-$10, Cats-$3, Mice-$.50 The total of... (answered by AnlytcPhil)

Can I please Have help with this, Thank You! Write the inequalities and describe the... (answered by ikleyn)

You have $100 and you want to spend all of it to buy exactly 100 pets- any combination of (answered by ankor@dixie-net.com)

Can I please have help with this. Write inequalities but don’t solve them please.... (answered by ikleyn,josgarithmetic)

A survey of 50 students found that 30 fad cats, 25 had dogs, 5 had white mice, 16 had... (answered by Edwin McCravy)

cupcakes are $4 and hot dogs are $3 each. you want to buy at least 5 items. you want to... (answered by ikleyn)