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
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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
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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. --> --> -->
