Answer to Question #12801 in Algebra for Ryan

Question

This problem was used a few times on the classic radio program The Life of Riley in the 1940s. Is there an answer?

A farmer sells 2 bushels of apples at X dollars a bushel. The next day the farmer sells 3 bushels of tomatoes for 1/3 the price of the apples. The day after he sells 1 ½ bushels of potatoes for 4/5 the price of the tomatoes. With the money he receives he buys 3 gallons of kerosene and 6 bags of fertilizer. If kerosene sells at $1 a gallon and fertilizer at $4 a bag, what's the price of … the apples?!

Answer 1

A farmer sells 2 bushels of apples at X dollars a bushel.
T = 2 * X.
The
next day the farmer sells 3 bushels of tomatoes for 1/3 the price
of the
apples.
T = 2 * X + 3 * (X / 3)
The day after he sells 1 ½ bushels of
potatoes for 4/5 the price of
the tomatoes.
T = 2 * X + 3 * (X / 3) + 1.5
* (4 * (X / 3) / 5)
With the money he receives he buys 3 gallons of kerosene
and 6 bags of
fertilizer:
C = 3 * 1 + 6 * 4 = 27
If T = C:
2 * X + 3
* (X / 3) + 1.5 * (4 * (X / 3) / 5) = 27
2 * X + X + 12 * X / 30 = 27
90 *
X / 30 + 12 * X / 30 = 27
102 * X = 810
X = $7.94