Two farmers were selling eggs. Each had 300 eggs. The first farmer was asking 1 cent for 2 eggs, while the second farmer was asking 1 cent for 3 eggs. They agreed to put their eggs together and sell 5 eggs for 2 cents. But 10 cents was lost in the transaction!. Explain what happened? Thanks.
+129840 If the first farmer only sells his eggs....he makes $1.50 = .5 cent = 1/2 cent for each egg
If the second farmer sells only his eggs.....he makes $1.00 = 1/3 cent for each egg
So the total made is 300 * (1/2) cents + 300 * (1/3)cents = [150 + 100 ] cents = 250 cents = $2.50
However....if they combine their products......they sell 600 eggs at 2/5 cents each = 600 * (2/5) cents = 240 cents = $2.40
To make the same profit by combining eggs........each egg should have been sold at [ 1/2 + 1/3 ] / 2 = 5/12 cents
Proof : 600 * 5/12 = 50 * 5 = 250 cents = $2.50
The first farmer was asking 1/2 cent for an egg, thus he should have received 1/2 x $3=$1.50(for 300 eggs). The second farmer was asking 1/3 cent for an egg, hence, he should have received 1/3 x $3 =$1.00 (for 300 eggs.) Therefore, both together should have received: $1.50 + $1.00 =$2.50. However, by combining their eggs, they got only 2/5 cents per egg. That is, the rate was changed, so that they received: 2/5 x $6.00 =$2.40 (for 600 eggs). Hence, together they lost:$2.50 -$2.40 =0.10 cents. However, the second farmer received $1.20 - $1.00 =0.20 cents more, while the first farmer lost: $1.50 - $1.20 =0.30 cents. Boy, pretty cheap eggs!!
