Proportions Word Problems Worksheet and Answers

A proportion is a set of 2 fractions that equal each other. This article focuses on how to use proportions to solve real life problems. Real World Uses of Proportions Modifying a budget for a restaurant chain that is expanding from 3 locations to 20 locationsCreating a skyscraper from blueprintsCalculating tips, commissions, and sales tax Modifying a Recipe On Monday, you are cooking enough white rice to serve exactly 3 people. The recipe calls for 2 cups of water and 1 cup of dry rice. On Sunday, you are going to serve rice to 12 people. How would the recipe change? If you’ve ever made rice, you know that this ratio—1 part dry rice and 2 parts water—is important. Mess it up, and you’ll be scooping a gummy mess on top of your guests crawfish à ©touffà ©e. Because you are quadrupling your guest list (3 people * 4 12 people), you must quadruple your recipe. Cook 8 cups of water and 4 cups of dry rice. These shifts in a recipe demonstrate the heart of proportions: using a ratio to accommodate lifes greater and smaller changes. Algebra and Proportions 1 Sure, with the right numbers, you can forgo setting up an algebraic equation to determine the amounts of dry rice and water. What happens when the numbers are not so friendly, however? On Thanksgiving, youll be serving rice to 25 people. How much water  do you need?Because the ratio of 2 parts water and 1 part dry rice applies to cooking 25 servings of rice, use a proportion to determine the quantity of ingredients. Note: Translating a word problem into an equation is super important. Yes, you can solve an incorrectly set up equation and find an answer. You can also mix rice and water together to create food to serve at Thanksgiving. Whether the answer or food is palatable depends on the equation. Think about what you know: 3 servings of cooked rice 2 cups of water; 1 cup of dry rice25 servings of cooked rice ? cups of water; ? cup of dry rice3 servings of cooked rice/25 servings of cooked rice 2 cups of water/x cups of water3/25 2/x Cross multiply. Hint: Write these fractions vertically to get the full understanding of cross multiplying. To cross multiply, take the first fractions numerator and multiply it by the second fractions denominator. Then take the second fractions numerator and multiply it by the first fractions denominator. 3 * x 2 * 253x 50Divide both sides of the equation by 3 to solve for x.3x/3 50/3x 16.6667 cups of waterFreeze- verify that the answer is correct.Is 3/25 2/16.6667?3/25 .122/16.6667 .12Whoo hoo! The answer 16.6667 cups of water is correct.   Ratio and Proportions Word Problem 1: The Brownie Recipe Damian is making brownies to serve at the family picnic. If the recipe calls for 2  ½ cups of cocoa to serve 4 people, how many cups will he need if there will be 60 people at the picnic? 37.5 cups What do you know?2  ½ cups 4 people? cups 60 people2  ½ cups/x cups 4 people/60 people2  ½/x 4/60Cross Multiply.2  ½ * 60 4 * x150 4xDivide both sides by 4 to solve for x.150/4 4x/437.5 x37.5 cups Use common sense to verify that the answer is correct.The initial recipe serves 4 people and is modified to serve 60 people. Of course, the new recipe has to serve 15 times more people. Therefore, the amount of cocoa has to be multiplied by 15. Is 2  ½ * 15 37.5? Yes. Ratio and  Proportions Word Problem 2: Growing Little Piglets A piglet can gain 3 pounds in 36 hours. If this rate continues, the pig will reach 18 pounds in  216  hours. What do you know?3 pounds 36 hours18 pounds ? hours3 pounds/18 pounds 36 hours/ ? hours3/18 36/x Cross Multiply.3 * x 36 * 183x 648 Divide both sides by 3 to solve for x.3x/3 648/3x 216216 hours Use common sense to verify that the answer is correct.A piglet can gain 3 pounds in 36 hours, which is a rate of 1 pound for every 12 hours. That means that for every pound a piglet gains, 12 hours will pass. Therefore 18 *12, or 216 pounds, is the correct answer. Ratio and  Proportions Word Problem 3: The Hungry Rabbit Denise’s rabbit can eat 70 pounds of food in 80 days. How long will it take the rabbit to eat 87.5 pounds? 100 days What do you know?70 pounds 80 days87.5 pounds ? days70 pounds/87.5 pounds 80 days/x days70/87.5 80/x Cross Multiply.70 * x 80 * 87.570x 7000 Divide both sides by 70 to solve for x.70x/70 7000/70x 100 Use Algebra to verify the answer.Is 70/87.5 80/100?70/87.5 .880/100 .8 Ratio and  Proportions Word Problem 4: The Long Road Trip Jessica drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles? 15.38 hours What do you know?130 miles 2 hours1,000 miles ? hours130 miles/1,000 miles 2 hours/? hours130/1000 2/x Cross Multiply.130 * x 2 * 1000130x 2000 Divide both sides of the equation by 130 to solve for x.130x/130 2000/130x 15.38 hours Use Algebra to verify the answer.Does 130/1000 2/15.38?130/1000 .132/15.38 is approximately .13

To What Extent Did Hitler Manipulate the German Population...

To what extent did Hitler manipulate the German population into following his Nazi regime? From 1933-1945 Adolf Hitler rose to the peak of his political power, by creating a stronghold over the German people. The use of oratory skills, in conjunction with his knowledge and use of propaganda and his suppression of details of the Holocaust, created a vibe of â€Å"electric excitement† for Germany. (Fritzsche, 1998) His targeting of the German minority and his radical push for anti-Semitism allowed Hitler to corrupt a weak and innocent nation. Manipulative leadership was a dominant force in the birth of his extremist beliefs and propagation, though this was assisted by the responsiveness of the negligent-minded German population to his plans.†¦show more content†¦Thousands upon thousands of Berliners cheered and celebrated as Hitler spoke of his new ambitions and plans for Germany. The crowd, which was labelled by a fellow member of the group as ‘deafening’, were excited by the Hitler’s enthusiasm; this had been lacking under the reign of Weimar democracy. (Fritzsche, 1998) The editor of Berlin’s Nazi newspaper, Der Angriff, Joseph Goebbels, remarked: â€Å"Uprising! Spontaneous explosion of the people. Indescribable!† (Fritzsche, 1998) Even though later in history we see Hitler’s ultimate motive to be his own rise in political hierarchy, his speech introduced himself to the German public as a populist and a â€Å"revolutionary political genius.† (Grunfield, 1974) Hitler endeavoured himself to all economical classes, whether it be the bourgeoisie, peasantry or the aristocracy; to them it appeared Hitler’s priority was to move Germany out of the current economic crisis and strive to develop Germany into a world superpower. The passion illustrated in Hitler’s goals was prevalent in his speeches, which led to the acceptance of a nation and the new title of â€Å"our Fuhrer† (Grunfield, 1974) Hitler’s use of Nazi propaganda was a major part of his scheme to empower himself to a weak nation; it gained him respect from the German people and endeared himself to them. The key, well documented, emphasis of the propaganda was the mass slaughter of allShow MoreRelatedThe Rise Of Nazism And The Holocaust1668 Words   |  7 Pages Adolf Hitler is one of these individuals. Hitler, the figurehead of the Nazi regime that led Germany to World War II, and instigated one of the most infamous genocides in history, the Holocaust. The impact Adolf Hitler had on history, namely, the rise of Nazism and the Holocaust is also due to a favourable set of circumstances that without them Hitler himself would not have been enough. 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Armenian Language Free Essays

anNadine Abo Laban 900113591 Gap paper 2 (Armenian Language) Introduction The guest speaker who graced us with her presence was Alyssah Depoya, who is of Armenian origin. According to Alyssah, all pure Armenians last names end with â€Å"yan† which acts as an indicator of whether the person is of pure Armenian origin. Armenia is a mountainous country located in the South Caucasus region in Eurasia. We will write a custom essay sample on Armenian Language or any similar topic only for you Order Now It is bordered by Turkey, Georgia, Azerbaijan and Iran (â€Å"Armenia†, n. d). Armenian people have a very rich and dense culture. It is one of the world’s oldest civilizations. Armenia was also the very first country to embrace Christianity as its religion. The Armenian culture has been shaped and influenced by many other countries due to the several invasions that their people had to endure. It has been conquered by the Persians, Greeks, Mongols, Byzantines, Ottomans, Arabs, Romans and Russians. The most brutal invasion was when the Ottoman Turks took over Armenia, killing its people and leaving them to starve to death. During the Ottoman take over between 600,000 and 1. 5 million Armenians were killed, leaving this massacre to be the very first genocide of the 20th century. Moreover, Turkey denies such a massacre having occurred and claims till this present day that death casualties were a minimum. Armenia houses a population of 3,140,000 citizens. However the total Armenian population is 5,924,320. They are wide spread over Azerbaijan, Canada, Egypt, Cyprus, Estonia, Georgia, France, Greece, Bulgaria, Lebanon, Palestine, Russia, united states and Syria (Lewis, 2013). Facts about the language According to my research from the Ethonologue and Wikipedia, there are 5,924,320 speakers of Armenian all over the world. The language belongs to the Indo-European language family and has several dialects. Most linguists identify the language as a separate branch under the indo European family. You can also call the Armenian language by Armjanski Yazyk, Ena, Ermeni Dili, Ermenice, Somkhuri. Before the creation of an Armenian alphabet, the Armenians used Greek and Aramaic characters. In 405 AD, the 36 characters of the Armenian alphabet were introduced. However, during the middle ages two more characters were introduced to the already existing alphabet so they can spell out borrowed foreign words. There are two different dialects of the Armenian languages used till this day. There is the Eastern classical Armenian, and the western, which is more commonly spoken by the people. The western dialect is mainly used outside of the republic of Armenia, whereas eastern is used both inside and outside the country. Report on the speaker’s presentation Fortunately, everything Alyssah informed us about coincided with my research. She was very entertaining and did not miss a detail about what we needed to know. How to cite Armenian Language, Papers