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Question 141950: When maple syrup is made the natural way, sap is gathered in late winter from sugar maple trees and within a few days is boiled down until a deliciously sweet and golden brown syrup is formed. When the sap comes from the tree, its sugar content is about 2.3% by weight and the rest is water. Suppose that 320 pounds of sap is boiled down until its weight in half of what it was originally (half of 320 pounds is 50% of 320 pounds or 160 pounds) What is the percent of sugar in the mixture after it has been reduced (boiled down) by
a) 50% b) 66.7% c) 80% d) P%
How much finished product will we get from these 320 pounds of sap if we know that the sugar content of Grade A Vermont Maple Sugar must be between 82 and 83%?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! When maple syrup is made the natural way, sap is gathered in late winter from sugar maple trees and within a few days is boiled down until a deliciously sweet and golden brown syrup is formed.
When the sap comes from the tree, its sugar content is about 2.3% by weight and the rest is water.
Suppose that 320 pounds of sap is boiled down until its weight in half of what it was originally (half of 320 pounds is 50% of 320 pounds or 160 pounds)
What is the percent of sugar in the mixture after it has been reduced (boiled down) by
a) 50%
Original wt. of sugar: 0.023*360 = 7.36 lb.
Percent sugar after 50% reduction in wt: 7.36/160 = 0.046 or 4.6%
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b) 66.7%
Percent sugar at 66.7% reduction: 7.36/[(1-0.667)*320] = 0.691 or 6.91%
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c) 80%
Percent sugar at 80% reduction: 7.36/[(1-0.8)*320] = 11.5%
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d) P%
Percent sugar at P% reduction: 7.36/[(1-P)*320]*100 %
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How much finished product will we get from these 320 pounds of sap if we know that the sugar content of Grade A Vermont Maple Sugar must be between 82 and 83%?
82 <= 7.36{(1-P)*320] <= 83
11.14 <= [(1-P)*320] <= 11.27
0.03482 <= 1-P <= 0.03524
-0.03524 <= P-1 <= -0.03482
0.96476 <= P <= 0.96518
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These are the reduction percentages.
You can figure out the weight of the liguid that remains after the reduction.
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cheers,
Stan H.
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