A+C=?

Algebra Level 2

Let A , B , C A,B,C satisfy the system of equations, A + B = C B + C = A + A + A + A + A \begin{aligned} A+B&=&C \\ B+C&=&A+A+A+A+A \end{aligned}

Then A + C A+C must be equal to which of the following expressions?

B + B B+B A + B A+B A A A + A + A A+A+A A + B + C A+B+C B + C B+C A + A A+A C + C + C C+C+C

Young Hwang by young hwang , 42, South Korea

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2 solutions

X X
Jul 11, 2018

C − B = A , C + B = 5 A C-B=A,C+B=5A ,we get C = 3 A , B = 2 A C=3A,B=2A .

A + C = 4 A = 2 A + 2 A = B + B A+C=4A=2A+2A=B+B

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Young Hwang
Jul 11, 2018

A+B=C,C-A=B.So A?B<C.(No minus)If A>B,5A=B+C,but A+B=C,so A<B<C.Go to 5A=B+C,if A is 1(A is smallest),5 is B+C,and you know B<C,(B,C)can be (1,4),(2,3).But A isn't B,1=1.So if A is 1,B is 2,and C is 3. So 1+3=2+2,B+B is answer.

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