SOLUTION: To create a chocolate blend, chocolate in two concentrations, 71% cocoa and 44% cocoa, are combined together. If 12 ounces of the 71% chocolate is used, how many ounces of the 44%

Question 1107393: To create a chocolate blend, chocolate in two concentrations, 71% cocoa and 44% cocoa, are combined together. If 12 ounces of the 71% chocolate is used, how many ounces of the 44% chocolate must be used to obtain a 56% chocolate blend?
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

(1) The traditional algebraic solution method....

"12 ounces of 71%, plus x ounces of 44%, equals (12+x) ounces of 56%"

I'll let you solve the equation to find the answer....

(2) By the method of alligation....

Once you understand it, this method gets you to the answer much faster and with less work.

As shown in this diagram...
the numbers in the first column are the percentages of the two ingredients (71%, 44%);
the number in the middle column is the percentage of the mixture (56%); and
the numbers in the third column are the differences, calculated diagonally, between the numbers in the first and second columns (71-56 = 15; 56-44 = 12).

When the calculations are performed this way, the two numbers in the third column show the ratio in which the two ingredients must be mixed.

So this diagram shows that the two ingredients must be mixed in the ratio 12:15; and since there are 12 ounces of the 71% chocolate, you need 15 ounces of the 44% chocolate.
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