SOLUTION: I have the answer to this problem but I need to be able to explain how to get the answer, other than guessing. Can you please help? One dog says to another, "If one of your fleas

Question 53596: I have the answer to this problem but I need to be able to explain how to get the answer, other than guessing. Can you please help? One dog says to another, "If one of your fleas jumped onto me, we'd have the same number." The other dogs says "But if one of yours jumped onto me , I'd have five times as many as you."
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I have the answer to this problem but I need to be able to explain how to get the answer, other than guessing. Can you please help? Fido says to Bozo, "If one of your fleas jumped onto me, we'd have the same number." Bozo says to Fido "But if one of yours jumped onto me , I'd have five times as many as you."
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Let "f" be the number of fleas on Fido.
Let "b" be the number of fleas on Bozo.
EQUATIONS:
1st: f+1=b-1
2nd: b+1=5(f-1)
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Rewrite to get:
3rd: f-b=-2
4th 5f-b= 6
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Subtract 3rd from 4th to get:
4f=8
f=2
Substitute into 3rd to solve for "b"
2-b=-2
b=4
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Check the answer in 4th, as follows:
5(2)-4=6
10-4=6
6=6
---------
So Fido has 2 fleas and Bozo has 4 fleas.
Cheers,
Stan H.

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