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# Philip has twice as many salamanders as Matt. If Philip

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Manager
Joined: 28 Jun 2004
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Philip has twice as many salamanders as Matt. If Philip [#permalink]  21 Aug 2004, 14:26
Philip has twice as many salamanders as Matt. If Philip gives Matt 10 of his salamanders, he will have half as many as Matt. How many each has?

Here, the first eq is P=2M. Now, Kaplan formulates the second equation as P-10 = 1/2(M+10).

My question is, why should the second eq not be P-10 = 1/2(M).

Any thoughts?
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Director
Joined: 20 Jul 2004
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If Philip gives Matt 10 of his salamanders, he will have half as many as Matt.

In the hypothetical situation, "Philip gives Matt 10 of his salamanders"
Then the situation of P is: P - 10 (he gave away 10)
Then the situation of M is: M + 10 (he got 10 new salamanders)

Their relation ship is "Phillip (P-10) will have half as many as Matt (M+10)"
P-10 = 1/2(M+10).
Senior Manager
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what you substract from Philip goes to Matt, that's why 10 needs to appear on both sides of the equation.

also, I would advise you to post a post a whole problem, and ask ppl to explain their answers, as opposed to giving it all out upfront. that's really the way to go in generating responses.
Manager
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the equation is

if matt has x then the other guy has 2x

therefore the equation is

2x-10 = x - x/2
if u solve it you will get x =8 and there 2x =16
cheers
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Jim

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I think Philip has 20 salamanders and Matt has 10 salamanders.

P = 2M

P - 10 = 1/2(M + 10)
P - 10 = 1/2M + 5
P = 1/2M + 15

1/2M + 15 = 2M
15 = 3/2M
M = 10
P = 2 * 10
P = 20

I think P = 16 and M = 8 is not possible with the other equation.

Correct me if I am wrong.

Regards,

Alex
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The second eq not is not P-10 = 1/2(M) because Matt has now M+10 not M.
cheers
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