Question 1150335
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By the traditional algebraic method for solving mixture problems like this, the solution could start like this:<br>
x pounds of coffee at $3.60 per pound, plus (40-x) pounds of coffee at $7.20 per pound, makes 40 pounds of coffee at $6.00 per pound.<br>
{{{x(3.60)+(40-x)(7.20) = 40(6.00)}}}<br>
That equation is solved by basic algebra, but the actual calculations are a bit tedious.<br>
Here is a much faster and easier way to solve a mixture problem like this, where only two things are being mixed.<br>
(1) The per-pound price of the mixture, $6.00, is two-thirds of the way from $3.60 per pound to $7.20 per pound.  (If it helps, look at the three numbers 3.60, 6.00, and 7.20 on a number line.  From 3.60 to 7.20 is 3.60; from 3.60 to 6.00 is 2.40.  2.40 is two-thirds of 3.60; 6.00 is two-thirds of the way from 3.60 to 7.20.)<br>
(2) That means two-thirds of the mixture must be the higher priced coffee.<br>
Unfortunately, the numbers don't work out "nicely" in this problem, because 2/3 of 40 pounds is not a whole number....<br>
ANSWER: 80/3 pounds, or 26 2/3 pounds, of the $7.20 per pound coffee and 40/3 pounds or 13 1/3 pounds, of the $3.60 per pound coffee.<br>