Question 1146450
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Standard algebraic solution method....<br>
x pounds at $5.90 per pound, plus (100-x) pounds at $6.40 per pound, equals 100 pounds at $6.18 per pound:<br>
{{{x(5.90)+(100-x)(6.40) = 100(6.18)}}}<br>
Straightforward; but some ugly calculations....<br>
A faster method, using only a couple of simple calculations, based on where the $6.18 per pound cost of the mixture lies between $5.90 and $6.40....<br>
(1) On a number line, look at where the 6.18 lies between 5.90 and 6.40.  5.90 to 6.40 is a difference of 0.50; 5.90 to 6.18 is a difference of 0.28.  0.28/0.50 = 28/50 = 56/100.<br>
(2) Therefore 56/100 of the mixture should be the higher priced walnuts.<br>
ANSWER: 56 pounds of the walnuts; 100-56 = 44 pounds of the almonds.