SOLUTION: Three boys are talking about how many sweets they each have. A: B has the most! B: If C gave me one sweet, I'd have twice as many as A does. C: It'd be better if B gave me two

Question 846445: Three boys are talking about how many sweets they each have.
A: B has the most!
B: If C gave me one sweet, I'd have twice as many as A does.
C: It'd be better if B gave me two sweets. Then we'd all have the same amount!
How many sweets are there in total?
I know the answer but the algebra is giving me trouble.
Answer by KMST(5347) (Show Source): You can put this solution on YOUR website!
= number of sweets A has.
= number of sweets B has.
= number of sweets C has.
We could even define .

The fact that C says
"It'd be better if B gave me two sweets. Then we'd all have the same amount!"
means .
That is 3 equations, but not independent, so it is worth 2 equations.

The fact that B says
"If C gave me one sweet, I'd have twice as many as A does."
means that .
With that last equation, we have 3 independent equations, and that's enough to solve.

We could even add and say we have a system of 4 linear equations, but why complicate when you can make it simpler.

Since two of the equations in have only A and B, I can solve for A and B with just two equations:
--> --> --> --> --> -->

Now I can use the results above and the equation I have not used to find C.
--> --> -->

Now, I can find the total
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