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Updated on: 02 Oct 2023, 11:53
Originally posted by Sajjad1994 on 08 Jan 2021, 09:00.
Last edited by BottomJee on 02 Oct 2023, 11:53, edited 2 times in total.
Last edited by BottomJee on 02 Oct 2023, 11:53, edited 2 times in total.
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Milk
Chocolate: 30 Dark
Chocolate: 45
Chocolate: 30 Dark
Chocolate: 45
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (01:59) correct
27%
(02:32)
wrong
based on 735
sessions
History
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Time
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A candy manufacturer is creating a new type of chocolate by combining dark chocolate and milk chocolate in a specific ratio. Dark chocolate contains 90% cacao and milk chocolate contains 40% cacao, and the new chocolate is to be 70% cacao. The manufacturer is doing a test run of 75 gallons of the new chocolate.
In the table below, identify the gallons of dark chocolate and gallons of milk chocolate that must be used to create 75 gallons of the new chocolate.
In the table below, identify the gallons of dark chocolate and gallons of milk chocolate that must be used to create 75 gallons of the new chocolate.
|
Milk Chocolate |
Dark Chocolate |
----------- |
| 15 | ||
| 25 | ||
| 30 | ||
| 45 | ||
| 50 |
ShowHide Answer
Official Answer
Milk
Chocolate: 30 Dark
Chocolate: 45
Chocolate: 30 Dark
Chocolate: 45
09 Jan 2021, 09:30
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Official Explanation
This can be solved two ways: the “tug of war” method and algebra (two equations). For the tug of war, simply figure out how far away the weighted average of 70% is from 90% and from 40%. 90 - 70 = 20, and 70 - 40 = 30. The ratio of dark:milk must then be 30:20, or 3:2. This is a 5 part ratio, and we know that we have 75 total gallons. Each part must then be worth 15 gallons. Dark: 3 parts * 15 gallons = 45 gallons. Milk: 2 parts * 15 gallons = 30 gallons.
To do it algebraically, set up two equations (using D for dark chocolate and M for milk chocolate): D + M = 75 and .9D + .4M = .7(75). We can then solve for the same values as above.
Milk Chocolate: 30
Dark Chocolate: 45
This can be solved two ways: the “tug of war” method and algebra (two equations). For the tug of war, simply figure out how far away the weighted average of 70% is from 90% and from 40%. 90 - 70 = 20, and 70 - 40 = 30. The ratio of dark:milk must then be 30:20, or 3:2. This is a 5 part ratio, and we know that we have 75 total gallons. Each part must then be worth 15 gallons. Dark: 3 parts * 15 gallons = 45 gallons. Milk: 2 parts * 15 gallons = 30 gallons.
To do it algebraically, set up two equations (using D for dark chocolate and M for milk chocolate): D + M = 75 and .9D + .4M = .7(75). We can then solve for the same values as above.
Milk Chocolate: 30
Dark Chocolate: 45
General Discussion
08 Jan 2021, 23:48
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Identify the gallons of dark chocolate and gallons of milk chocolate that must be used to create 75 gallons of the new chocolate.
Writing the allegation for the mixture in terms of cacao content :
Dark Chocolate Milk Chocolate
90 40
70(mix)
70-40 = 30 90-70 = 20
Thus, Dark:Milk = 3:2
In 75 gallon of the new chocolate :
Dark chocolate = 3/5 x 75 = 45 gallons.
Milk chocolate = 2/5 x 75 = 30 gallons.
Writing the allegation for the mixture in terms of cacao content :
Dark Chocolate Milk Chocolate
90 40
70(mix)
70-40 = 30 90-70 = 20
Thus, Dark:Milk = 3:2
In 75 gallon of the new chocolate :
Dark chocolate = 3/5 x 75 = 45 gallons.
Milk chocolate = 2/5 x 75 = 30 gallons.
