SOLUTION: Dexter has 36 pets. He has 3 times as many fish as mice and half as many cats as mice. How many of each pet does Dexter have? thank you

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Question 323212: Dexter has 36 pets. He has 3 times as many fish as mice and half as many cats as mice. How many of each pet does Dexter have?
thank you
Answer by QH(50) About Me  (Show Source):
You can put this solution on YOUR website!
First assign variables. B/c both the cats and fish are compared to mice,
let MICE = x
"3 times as many fish as mice"
let FISH = 3x
"half as many cats as mice"
let CATS = 1/2x
So add all three and set equal to the total pets
x%2B3x%2B%281%2F2%29x=36
solve for x
4x%2B%281%2F2%29x=36
%288%2F2%29x%2B%281%2F2%29x=36
%282%2F9%29%2A%289%2F2%29x=36%2A%282%2F9%29
x=%2872%2F9%29 or 8
x = 8 MICE
3x = 24 FISH
1/2x = 4 CATS
*check*
8%2B24%2B4=36
36=36