# Answer on Algebra Question for Ryan

Question #12801

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?!

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?!

Expert's answer

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

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

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