Candy and boxes

We have some candy and empty boxes. When we put ten sweets in boxes, two candies and eight empty boxes will be left. When of eight, there will be six candies and three boxes left. How many candy and empty boxes are gone when we put nine sweets into a box?

Correct answer:

x =  51
y =  11

Step-by-step explanation:

$$\begin{gathered} b-(k-8)\cdot 10=2 \\ b-(k-3)\cdot 8=6 \\ b-10k=-78 \\ b-8k=-18 \\ Row2-Row1\to Row2 \\ b-10k=-78 \\ 2k=60 \\ k=\frac{60}{2}=30 \\ b=-78+10k=-78+10\cdot 30=222 \\ b=222 \\ k=30 \\ b-(k-y)\cdot 9=x \\ 222-(30-y)\cdot 9=x \\ x=9n+6 \\ y=n+6 \\ n\ge 2 \\ 9n+6\le 222 \\ n{\le }_{24} \\ 2\le n{\le }_{24} \\ n=5 \\ x=9\cdot n+6=9\cdot 5+6=51 \end{gathered}$$

$y=n+6=5+6=11$

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