The number of yellow, red, and blue pens in a box is in the ratio 2:5:7. If 18 yellow pens, 12 red pens, and some blue pens are added to the box, the ratio of yellow, red, and blue pens becomes 3:6:8. Determine the number of blue pens added.

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Accepted Answer

1. Let the initial counts be $2k,\;5k,\;7k$. 
2. After adding we have $2k+18,\;5k+12,\;7k+x$ and ratio $3:6:8$. So $5k+12=2(2k+18)$. Solve: $5k+12=4k+36$ so $k=24$.
3. Then $2k+18=66=3t$, so $t=22$.
4. Now $8t=176=7k+x=168+x$ so $x=8$.

FINAL_ANSWER: b

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