word problem from kangaroo math contest

Question

Albert and Ben each have several marbles. if Albert gives 6 of his marbles to Ben, they will have the have the same amount of marbles. if Albert gives half of his marbles to Ben, then Ben will have 8 more marbles then Albert will have. how many marbles in total do they have?

The correct answer is 28.

When I solved it, I got 14 marbles for Albert and 8 for Ben which in total is 22 but it wasn't any of the 5 options so I want to know how they got 28.

How I tried solving it: first, I put a random number of marbles that Albert could have. lets say I put 18. then I subtracted 6 from it to get the number of marbles Ben could have as it says in the first statement $(18-6=12).$ After that, I divided the amount of marbles Albert has by 2 $(18/2=9).$ Then I added 9 to 12 to get the amount of marbles Ben could have. Then I subtracted 9 from 18 and I got 9. If that subtracted from 12 would give a number less then 8, I would lower the amount of marbles Albert could have in the beginning and start over. If it was higher then 8, I would up the amount Albert could have in the beginning and start over. I would do this until it matched the 2 statements in the question.

Answer 1

Let Albert have $A$ marbles and Ben have $B$ marbles. The two statements can then be written as \begin{eqnarray*} A-6=B+6 \\ \frac{A}{2} + 8 = \frac{A}{2} +B. \end{eqnarray*} Should be easy from here ?

Answer 2

Let set $x$ the number of Albert's marbles and $y$ the number of Ben's marbles. Since we have two unknowns, we need two equations. Then the statements gives us $$x-6=y+6$$ $$\frac x2+8=y+\frac x2$$ Solving for $x$ and $y$, we have $$y=8\text{ and }x=20$$ Thus the marbles' total is $28$.

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Simplifier proof would be the second statement give us how manyarbles Ben have. Since Albert splits His marbles in two and give half to Ben, the difference between the two is the amount Ben has. Then Ben has $8$ marbles and the other value follows from the first statement.