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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.
Fresh tomatoes cost $.95 per pound to grow from seed to harvest. If they are sold fresh, packaging costs $.35 per pound and 35% of the whole quantity goes to waste during handling. The farmer sells the fresh tomatoes to a wholesaler for $2.15 per pound. If they are sold dried, the drying/packaging process costs $.55 per fresh pound and the mass of tomatoes decreases through dehydration by 75%. What price per pound should the farmer sell the dry tomatoes for, in order to make the same percent profit as on the fresh tomatoes?
|Product||Cost Fresh||Handling||Weight loss||Cost per lb||Sell per lb||Net Profit|
To find the final cost per lb, we proceed as follows:
After a weight loss of 35%, only 65% of the mass is left, therefore the cost per lb. can be found from the proportion:
For the dry tomatoes:
The net profit is not the same as the percent profit: a net profit of $.15 cents over a cost of $2.00 must be in the same ratio as a net profit of p-6.00 over a cost of $6.00:
The selling price for the dry tomatoes must be $6.45/lb.