A panel has 6 members. The chairperson's age is twice the average age of the other five members, and the six ages add up to 224 years. How old is the chairperson?

Let the other five average a years, so they total $5a$ and the chairperson is $2a$. Then $5a+2a=224$, so $7a=224,a=32$ and the chairperson is 64. (Check: the other five total 160 and 160 + 64 = 224.) 32 is the average age of the other five, the value a, taken before doubling. 44.8 is 224/5, dividing the whole total by the wrong count. 112 halves the 224, applying 'twice' to the total rather than to the average of the other five - the chairperson is twice ONE average, not half of everything.