A candy manufacturer is creating a new type of chocolate by combining

Question

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.

Sajjad1994 · Accepted Answer

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

Sumi1010 · Answer

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.

Deepakjhamb · Answer

lets analyze the stem

by alligation method we have

40% ------ 70%-------- 90%

ratio of MC /DC mixed = ( 90-70) /(70-40)

MC/DC = 20/30 =2/3

SO in 75 gallons of new chocolate we need MC = 2/5 * 75 = 2* 15 = 30 Gallons

DC = 3/5 *75 = 3*15 =45 Gallons

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

so answer is Milk chocolate = 30
Dark Chocolate = 45

rocky620 · Answer

Dark Chocolate = DC
Milk Chocolate = MC

Let he mix x gallons of DC & y gallons pf MC. Also it is given that the total qty of test run is 75 gallons, so x+y = 75
Cacao in 1 gallon of DC = 90% / .90, so in x gallons = .90x
Cacao in 1 gallon of MC = 40% / .40, so in y gallons = .40y

Mixing these two qtys will give the final mixture with 70% / .70 Cacoa. So,

.90x+.40y = .70 (x+y)
.90x+.40y = .70x+.70y
.20x=.30y
 \frac{x}{y}  =  \frac{.30}{.20}  =  \frac{3}{2} 
So he has to mix DC & MC in the ratio of 3:2, so that the resultant will have 70% Cacao

From the below values only two combinations, whose sum is 75, are possible
50+25 & 45+30, only 45+30 is in the ratio of 3:2

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.

15
25
  30 - Milk Chocolate
45 - Dark Chocolate  
50

TarunKumar1234 · Answer

From the figure below, multiplier = x= 15

Dark chocolate  required to mix = 3x = 3*15 =  45 gallons 
 Milk chocolate  required to mix = 2x = 2*15 =  30 gallons

Sajjad1994 · Answer

OA has been posted:

Milk Chocolate: 30, Dark Chocolate: 45

This is a medium level question, Good effort by  TarunKumar1234 . As expected everyone got this correct. Official explanation will be posted with in a few minutes.

bot00078 · Answer

https://gmatclub.com/forum/download/file.php?id=86345 GMAT-Club-Forum-49lim77i.jpeg

A candy manufacturer is creating a new type of chocolate by combining

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