Question 1149228
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Tutor @josgarithmetic loves responding to questions involving mixture problems like this by using algebra and a whole bunch of variables to derive an ugly-looking formula for getting the answer.<br>
The method I like to use to solve these kinds of problems is essentially the same -- but it uses logical reasoning and a bit of simple mental arithmetic to get to the answer.<br>
Here is my preferred method of solving the problem.<br>
(1) The difference between the per-pound prices is 98-68 = 30 cents.
(2) The difference between the lower per-pound price and the per-pound price of the mixture is 75-68 = 7 cents.
(3) Those two simple calculations tell us that the price of the mixture is 7/30 of the way from the lower price to the higher price; and that means that 7/30 of the mixture must be the higher priced sunflower seeds.<br>
ANSWER: (7/30) of 40 pounds is 28/3 pounds, or 9 1/3 pounds.  The 40-pound mixture should be made using 9 1/3 pounds of sunflower seeds and 30 2/3 pounds of birdseed.<br>