A jam maker wants to increase the sugar content in a batch of strawberry jam. The batch currently contains 50 liters of strawberry puree with 5% sugar concentration. The maker decides to add 10 liters of sugar syrup that is 40% sugar by weight. What is the final sugar concentration of the jam after mixing? Solution: Initial volume of jam = 50 liters Initial sugar concentration = 5% (5 grams of sugar per 100 grams of Jam) Amount of sugar in the jam Initially 5% of 50 liters = 2.5 liters of sugar. Volume of sugar syrup added = 10 liters Sugar concentration in the syrup = 40% (40 grams of sugar per 100 grams of syrup) Amount of sugar in the syrup = 40% of 10 liters = 4 liters of sugar Total volume of the mixture 50 liters +10 liters = 60 liters.
Answer (1)
1. Initial sugar in the jam: - Initial volume of jam = 50 liters - Initial sugar concentration = 5% - Amount of sugar in the jam = 5% of 50 liters = \( 0.05 \times 50 = 2.5 \) liters2. Sugar added from the syrup: - Volume of sugar syrup added = 10 liters - Sugar concentration in the syrup = 40% - Amount of sugar in the syrup = 40% of 10 liters = \( 0.40 \times 10 = 4 \) liters3. Total sugar after mixing: - Total sugar = Sugar in jam + Sugar in syrup = \( 2.5 + 4 = 6.5 \) liters4. Total volume after mixing: - Total volume = Initial volume of jam + Volume of syrup = \( 50 + 10 = 60 \) litersSo, the final sugar concentration of the jam after mixing is approximately 10.83%
