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Mixture Problems By: Jacob Hoadley What is a mixture problem? • Word problems where items or quantities of different values are mixed together Mixture Problems + Real Life • After learning quite a bit of information about mixture problems, I’ve found that they can be most useful to business owners who are trying to figure out what they need to use to make a certain profit • Mixture problems can also be used for all kinds of science problems, chemistry in particular Problem #1 • Mr. Wilson wrote down his daily black cow root beer float sales for the last week. He had sold 414 floats at $2.15 each. The ingredients for the floats cost $1.08 per float. How much profit did he make last week? Problem #1 answer • • • • 414*2.15 = 890.1 414*1.08 = 447.12 890.1 – 447.12 = 442.98 Mr. Wilson’s total profit was $442.98 Problem #2 • 9 lbs of mixed nuts containing 55% peanuts was mixed with 6 lbs of another kind of mixed nuts that contains 40% peanuts. What percent of the new mixture is peanuts? • .55*9 + .40*6=15x • 4.95 + 2.4 = 15x • 7.35 = 15x • X = 7.35/15 • X = .49 or 49% of the new mix is peanuts Problem #2 answer • • • • • .55*9 + .40*6=15x 4.95 + 2.4 = 15x 7.35 = 15x X = 7.35/15 X = .49 or 49% of the new mix is peanuts Problem #3 • Brand X sells 21 oz. bags of mixed nuts that contain 29% peanuts. To make their product they combine Brand A mixed nuts which contain 35% peanuts and Brand B mixed nuts which contain 25% peanuts. How much of each do they need to use? Problem #3 answer • • • • • • Let a = ounces of brand A nuts used Let b = ounces of brand B nuts used .35a +.25b/21 = .29 .35a + .25b = .29 * 21 (1) .35a + .25b = 6.09 (2) A + B = 21 #3 continued • Now we multiply both sides of (2) by .25 and then we subtract (2) from (1) • 21*.25 = 5.25 • (1) .35a + .25b = 6.09 • (2) .25a + .25b = 5.25 • 6.09 – 5.25 = .84 = .1a • A = 8.4 #3 continued • • • • • A + B = 21 8.4 + B = 21 21 – 8.4 = 12.6 B = 12.6 8.4 + 12.6 = 21