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# The missing dollar

## Question

Two women were selling marbles in a market place -- one at three for a dollar and the other at two for a dollar. One day both of them returned home when each had thirty marbles unsold. They put together the two lots of marbles and handing them over to a friend asking her to sell them at five for 2 dollars. According to their calculation, three for one dollar and two for one dollar makes it five for two dollars.

Now, they were expecting to get 25 dollars for the marbles, as they would have got if sold separately. But much to their surprise they got only 24 dollars for the entire lot.

Where did the one dollar go? Can you explain they mystery?

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Here goes,

The women had 60 marbles total. They sold them at 5 for \$2. 60/5=12. 12X\$2=\$24.

Peace

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The friend sold sixty marbles at 40 cents apiece [5 marbles = \$2] and got \$24.

But the women expected \$25.

The mystery is not where is a missing dollar; it's why did they expect \$25?

They wanted their friend to get the same amount as if they had sold the sixty marbles separately:

[1] one would have got \$10 [30 marbles/3 marbles/\$1]

[2] the other \$15 [30 marbles/2 marbles/\$1]

[Total] \$25 for all sixty.

They should have told her to sell for the average of their prices.

Equal numbers of marbles [30] at avg price would have done it.

AVG [33.333 cents apiece, 50 cents apiece] = 41.667 cents apiece * 60 marbles = \$25.

What they averaged was the number of marbles that each women would have sold if they had had equal dollar sales.

But if they had had equal dollar sales, more marbles would have been sold by the first woman, at a lower than average price.

And the combined sales would have been lower: \$24 to be exact.

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