{"id":6999,"date":"2014-05-08T17:59:14","date_gmt":"2014-05-08T17:59:14","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6999"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-review-of-weighted-averages-and-mixtures","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-weighted-averages-and-mixtures\/","title":{"rendered":"Math Review of Weighted Averages and Mixtures"},"content":{"rendered":"

Overview:<\/h3>\n

Calculating the values for weighted averages and mixtures is common to many fields, from education to chemistry.\u00a0 The calculations for both require attention to the amount of each quantity and its relationship to the whole.<\/p>\n

Weighted Averages:<\/h3>\n

Suppose a student takes 6 math tests with an average of 87.\u00a0 The final is worth 2 regular tests, and the score on that test is 95.\u00a0 What is their average for the class?\u00a0 In order to solve the problem, the average of 87 is weighted at 6\/8 and the average of 95 is weighted at 2\/8, and then they are added together.\u00a0 Using equivalent fractions, 6\/8 is equal to .75, and .75 times 87 is 65.25, and 2\/8 is equal to .25, and .25 times 95 is 23.75.\u00a0 The final average is 65.25 +23.75, or an average of 89.<\/p>\n

Varying Rates:<\/h3>\n

Suppose a trip takes one speed going and another speed returning.\u00a0 The distance will be the same in both cases, but the percentage of time it takes will be different, and will also be a weighted averages type of problem.\u00a0 The distance between Metropolis and Gotham City is 240 miles.\u00a0 The Batmobile drove within the speed limit at 60 mph to get from Metropolis to Gotham City.\u00a0 However, traffic was bad on the way back, and the Batmobile could only go 40 mph.\u00a0 What is the average speed for the round trip? It took 4 hours to get there (because 240\/60 is 4) and 6 hours to get back (because 240\/40 is 6), for 10 hours total.\u00a0 Using weighted averages, 4\/10 (.60) + 6\/10(40) is equal to 48 miles per hour on average.\u00a0 (It would be much faster to fly.)<\/p>\n\n\n\n
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Figure 1:\u00a0 Holy weighted averages, Batman!\u00a0 Will we ever get through this traffic?<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Mixtures:<\/h3>\n

Mixtures are solved in a similar method to weighted averages.\u00a0 Cologne is a solution of perfume oil diluted with alcohol.\u00a0 It is less expensive because the alcohol is much less expensive than the perfume oil.\u00a0 Suppose 5 ounces of perfume oil at 100.00 per ounce are mixed with 25 ounces of alcohol at 3.00 per ounce.\u00a0 How much is the resulting mixture worth per ounce?\u00a0 The total amount of cologne is 30 ounces, so 5\/30 (100.00) + 25\/30 (3.00) = 16.67 + 2.50, or about $19.17 per ounce.<\/p>\n

Multiple Mixtures:<\/h3>\n

The weighted average of more than two quantities is similar to finding the weighted average of two quantities.\u00a0 The Candy Crunch Company is always looking for new confections. \u00a0Suppose there is a mixture of 7 ounces of popcorn at 1.00 an ounce, 2 ounces of peanuts at 3.00 an ounce, and 1 ounce of chocolate chips at 2.00 an ounce.\u00a0 The resulting mixture of popcorn-nut-chocolate goodness will sell for .7(1.00) + .2(3.00) +.1(2.00), or 1.50 an ounce.<\/p>\n\n\n\n
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Figure 2:\u00a0 The weighted average with more than two ingredients is similar to the weighted average with 2 ingredients.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

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Overview: Calculating the values for weighted averages and mixtures is common to many fields, from education to chemistry.\u00a0 The calculations for both require attention to the amount of each quantity and its relationship to the whole. Weighted Averages: Suppose a student takes 6 math tests with an average of 87.\u00a0 The final is worth 2 […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[1132,2690],"class_list":["post-6999","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-mixtures","tag-weighted-averages"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6999","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6999"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6999\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6999"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6999"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6999"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}