Question 1107393
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(1) The traditional algebraic solution method....<br>
"12 ounces of 71%, plus x ounces of 44%, equals (12+x) ounces of 56%"<br>
{{{12(.71)+x(.44) = (12+x)(.56)}}}<br>
I'll let you solve the equation to find the answer....<br>
(2) By the method of alligation....<br>
Once you understand it, this method gets you to the answer much faster and with less work.<br>
{{{matrix(3,3,71,"",12,"",56,"",44,"",15)}}}<br>
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).<br>
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.<br>
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.