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Solving equation

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Solving equation [#permalink] New post 23 Apr 2010, 23:13
Given a, b and c are prime numbers, solve the system of equations
a(b + c) = 224
b(a + c) = 338

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Re: Solving equation [#permalink] New post 24 Apr 2010, 01:59
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a(b + c) = 224 = 32*7
=> a must be 7 and b+c = 32 as a is prime

b(a + c) = 338 = 2*13*13 => b must be either 2 and a+c=169 or b = 13 and a+c = 26

since b = 2 and b+c=32 => c =30 but this is not true

so b must be 13 => b+c=32 => c = 19

hence a = 7, b=13 c = 19

you can verify this by a+c = 19+7 = 26
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Re: Solving equation   [#permalink] 24 Apr 2010, 01:59
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