Question 1173877
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Here is a non-algebraic method for solving this kind of two-part mixture problems that, with a little practice, can get you to the answer much faster and with less effort than setting up and solving an algebraic equation.<br>
Look at the three prices per pound of the two ingredients and the mixture on a number line: 0.80, 1.70, and 2.90.
Determine by simple calculations that 1.70 is 0.90/2.10 = 3/7 of the way from 0.80 to 2.90.
That means 3/7 of the mixture is the $2.90 per pound caramels, so 4/7 is the $0.80 per pound popcorn.
And since the 4/7 of the mixture that is popcorn is 4 pounds, the 3/7 of the mixture that is caramels is 3 pounds.<br>
ANSWER: 3 pounds of caramels<br>
CHECK:
4(0.80)+3(2.90) = 3.20+8.70 = 11.90
7(1.70) = 11.90<br>