Answers 229- HORSES AND BULLOCKS
We have to solve the indeterminate equation 344x = 265y + 33. This is
easy enough if you know how, but we cannot go into the matter here. Thus x
is 252, and y is 327, so that if he buys 252 horses for $344.00 apiece, and 327
bullocks for $265.00 apiece, the horses will cost him in all $33.00 more than
the bullocks.
- BUYING TURKEYS
The man bought 75 turkeys at 80¢ each, making $60.00. After retaining 15
he sold the remaining 60 at 90¢ each, making $54.00, as stated. He thus made
a profit of 1O¢ each on the 60 birds he resold.
- THE THRIFTY GROCER
He must have had 168 each of dollar bills, half dollars, and quarters,
making a total of $294.00. In each of the six bags there would be 28 of each
kind; in each of the seven bags 24 of each kind; and in each of the eight bags,
21 of each kind.- THE MISSING PENNY
The explanation is simply this. The two ways of selling are only identical
when the number of apples sold at three for a penny and two for a penny is
in the proportion of three to two.
Thus, if the first woman had handed over 36 apples, and the second woman
24, they would have fetched 24¢, whether sold separately or at five for 2¢.
But if they each held the same number of apples there would be a loss when
sold together of l¢ in every 60 apples. So if they had 60 each there would be
a loss of2¢. If there were 180 apples (90 each) they would lose 3¢, and so on.
The missing penny in the case of 60 arises from the fact that the three a
penny woman gains 2¢, and the two a penny woman loses 3¢.
Perhaps the fairest practical division of the 24¢ would be that the first
woman receives 9l6¢ and the second woman 14'12, so that each loses l6¢
on the transaction.