Fruit Juice Manufacturers HARD MATH PROBLEM PLEASE HELP?
HARD MATH PROBLEM PLEASE HELP? - fruit juice manufacturers
A soft drink manufacturer announces orange drink as "natural flavor", even if only 5% of orange juice. A new federal regulation requires the so-called "natural flavor" of a drink should contain at least 10% fruit juice. How much pure orange juice from the manufacturer to add 900 liters of orange soda in order to be adapted to this new scheme? The answer is 50 gallons, but it would be 45 gallons. I do not know how to get the answer.
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9 comments:
She took the 5% of 900 gallons and will be multiplied by 2 to 10%. However, if you orange juice, add the total volume is too high. 90 gallons total volume of 945 gallons now has 10%. That was his mistake. Hope u get it:)
However, if u add 50 liters of orange juice is now at 95 liters, while the total volume is 950 liters, which is 10%.
Operation:
The volume of juice added by X.
His fluid remains constant, p. 855 gallons.
(900 + X) x 0.9 = 855
810 + 0.9 x = 855
0.9 x = 45
X = 50
She took the 5% of 900 gallons and will be multiplied by 2 to 10%. However, if you orange juice, add the total volume is too high. 90 gallons total volume of 945 gallons now has 10%. That was his mistake. Hope u get it:)
However, if u add 50 liters of orange juice is now at 95 liters, while the total volume is 950 liters, which is 10%.
Operation:
The volume of juice added by X.
His fluid remains constant, p. 855 gallons.
(900 + X) x 0.9 = 855
810 + 0.9 x = 855
0.9 x = 45
X = 50
This is certainly a difficult problem, but I will show how easily the problem step by step:
Let x = the first 900 gallons = 95% juice is not total = 0.95T (T is described below).
Y = number of extra to the gallon of X should be added, adjusted to 10% natural fruit juice.
Let T = total number of liters of freshly squeezed juice at the end = 90% + 10% of natural juice = 100% = x + y
Setting the equation and replaced Ablova used to resolve and to:
Start with T = x + y
T = 900 + y = y = 0.95T + 0.95 (x + y) + Y
900 + y = 0.95 x + y + 0.95y
900 = 0.95x + 0.95y
900 = 947.37 + 0.95y
0.95y = -47.37
y = -49.86 gallons
Gallons negative does not make sense, then you must accept the absolute value:
| Y | = | -49.86 | gallon = 49.86 gallons = 50 gallons
So your answer is 50 gallons.
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Check your answer:
Note that the first x = 900 gallons or 95% T, where
T = x + y = 900 + 50 = 950.
Therefore, x / D = 900/950 = 95%.
I hope this helped.
Let x = gallons of pure orange juice in the 900 liters orange soda
[(900 (0.05) + x) / (900 + x)] 100 = 10
(45 + x) / (900 + x) = 10/100
45 + x = 0.1 (900 + x)
45 + x = 90 - 0.1x
x = + 0.1 x 90-45
0.90x = 45
x = 45/0.90
x = 50 gallons RESPONSE
Hope this helps.
Teddy Boy
Let x = gallons of pure orange juice in the 900 liters orange soda
[(900 (0.05) + x) / (900 + x)] 100 = 10
(45 + x) / (900 + x) = 10/100
45 + x = 0.1 (900 + x)
45 + x = 90 - 0.1x
x = + 0.1 x 90-45
0.90x = 45
x = 45/0.90
x = 50 gallons RESPONSE
Hope this helps.
Teddy Boy
5% (900) = 45 gallons
Add an additional 5% = 10% = 45 + 45 = 90 gallons in a 10% fruit juice
Adding another 5% -10% = 45 gallons is more than 5%
So, 900 liters of juice = 10% + 90% other
which 45 liters of orange juice has about 855 liters of liquid
(900 + X) *. 9 = 855
900 + X = 855/.9
900 + X = 950
X = 950-900
X = 50 liters of orange juice should be added
.05 (900) + 1 (x) = (900 + x) (.1)
45 + x = 90 x + .1
9 X = 45
x = 50
900 (.5) + 50 = 950 (.1)
45 + 50 = 95
I'm confused and I thought it would be 45!
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