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# Math 160 1-3 - 1-4 Notes Math 160

Marshall

GPA 3.8

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This 0 page Class Notes was uploaded by Jason DeHaven on Wednesday February 17, 2016. The Class Notes belongs to Math 160 at Marshall University taught by Puppalo-Cody in Winter 2016. Since its upload, it has received 23 views. For similar materials see Applied Mathematical Reasoning in Criminal Justice at Marshall University.

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Date Created: 02/17/16

SECTION 13 AND 14 RATIO AND PROPORTION AND WORD PROBLEM STRATEGIES Ratio the quotient of the first number divided by the second from one number to another number You can say 7 to 8 up to 4 different ways 1 Use a ratio sign 78 7 to 8 2 Use a division symbol 7 e 8 7 divided by 8 3 Write as a fraction 78 seveneighths 4 Write as a decimal 0875 eight hundred seventy five thousandths m Finding Ratios 1 Express the measurements in the same unit 2 Divide the two measurements by writing them as a fraction 3 Reduce the fraction 4 Express the fraction using a ratio sign Examples for Finding Ratios are below a 20min 2hours 20min 120min 20120 16 1 6 b 6 feet 120 inches 6 feet 10 feet 610 35 3 5 c 6 weeks 3 days 42 days 3 days 423 141 14 1 A ratio is a comparison of two numbers having the same units of measure These like units will cancel leaving all ratios as pure fractions A rate is similar to a ratio but the units of measure are different Due to the units being different they won t cancel but are reduced down to the unit rate with the denominator being 1 a 435 for 3 lbs of cheese 435 3 lbs or 435 3 lbs 145 1 lbs or 145 1 lbs b 544 miles in 8 hours 544 miles 8 hours or 544 miles 8 hours 68 miles 1 hour or 68 miles 1 hour c 3375 miles on 135 gallons of gas 3375 miles 35 gallons or 3375 miles 35 gallons 25 miles 1 gallon or 25miles1 gallon Proportion an equation that states that 2 ratios are equal Examples 4623 and 1820910 These above are equal to each other The proportion ab old can be written as ab cd Both forms of the proportions are read a is to b as c is to d The first and last terms of a proportion are called the extremes and the second and third terms are called the means When you use cross multiplication on the proportions you can see that the two fractions are equal For example as from above we have 46 23 4312 and 6X2 12 mm UOOK IS an lowan farmer partucnpatlng In a field test using a new type of hybrid corn His first crop yielded 5691 bushels of corn last year from a 35acre field if he plants the same type of corn in a 42eacre field this year assuming adequate growing conditions how many bushels should he expect to harvest Let x the number of bushels of corn The given rate is 35 acres yields 5691 bushels Set up a proportion using this rate to solve for the unknown 35 acres 5691 bunches 42 acres x 35x 425691 35X 239022 X 682902 bunches Therefore he should expect to harvest approximately 6829 bushels of corn from a 42 acre field Find x in the following Proportion 2x7 814 28X 56 X2 New Problem House pians are drawn to scaie which is stated as a rate on a biueprint If a house pian is drawn to a scale of 1 in 8 ft give the true dimensions of a room if the biueprint shows a length of 23 in and a width of 11 5 in 4 16 18 275x and 18 19375x X 22 feet and x 155 feet To be successful you must know the fundamental rules of algebra and be able to use them with common sense Iive Steps to SOIVH IQ Word Prontems Step 2 Step 3 Step 4 Step 5 Read the problem Put down your pencil and read the problem all the way through Decide what quantity the problem is asking you to nd Remember that mathematics has a special language of its own It may he a good idea to circle the key words that you nd in the problem Use Table 14 as a reference Select a variable to represent one off the quantities in the problem Then write expressions for other unknown quantities in terms of the selected variable The statement immediately preceding the question mark is usually the key statement Read it carefully Translate the word problem into a mathematical statement equationmodel that describes the conditions of the problem llt may be helpful to start with a word equation and then substitute the variables and given values in place of the words they represent This is the tough step Look for patterns or try to match a new problem to a similar one that you have already worked Guessing is allowed here Using algebra solve the equation you have written for the valuets that is are required Check your solution in the origier WOFdi g of the problem not in your derived equation Is your answer reasonable For word problems you have indictor words that determine what kind of operation you are being directed to do Examples Addition plus more more than sum total increased by added to sum of increase of Subtraction less minus take away subtract subtracted from difference less than fewer decreased by and loss of Multiplication product double triple of twice times Division divvied by goes into quotient divide per Equals gives are is the same as equals yields The Word AND This word is commonly shown in word problems and isn t one of those words listed for indicators because it is usually used to show the location of where the operation will take place Examples 0 The sum of 7 and 5 This comes out to be 75 0 The difference between 7 and 5 This comes out to be 75 First Word Problem Read it One number is 12 more than another number The sum of the two numbers is 156 What are the two numbers Then put x variable for the first number Then let x12 be the second number Then you will go into creating the equation xx12156 0 Then you will simplify 2x12156 0 Then subtract 12 from both sides 2x144 0 Then divide x72 0 So now you have your first So add 12 to 72 721284 o The two numbers are 72 and 84 which add up to be 156 Consecutive Integers numbers one right after another can be negative or positive Such as 5 6 7 8 and 11 10 9 and 8 The sum of four consecutive integers is 2 What are the integers Let x be the first integer Then x1 is the next consecutive integer X2 is next then X3 is next SO the equation is xx1x2x32 Simplify 4x62 Subtract 6 from both sides 4x8 Divide both sides by 4 x2 Check your work Plug in 2 to x 4262 Multiply 42 8 86 2 both sides are equal This is correct 22 OOOOOO The sum of three consecutives odd integers is 1503 What are the integers xx2x41503 Make your equation based off the question Simplify 3x61503 Subtract 6 3x1497 Divide by 3 x499 Plug in 499 for the other values to check your work x2 4992501 X44994503 499501 503 1503 Add the solutions and you get 1503 which is equal Determining an Original Value after a Percent Increase Read the Question In January Mariana s car insurance premium was 6698 This was a 1 price increase from her monthlv cost last vear What was the monthly cost of her car insurance last year Start with variable x x001x6698 0 Why are there two x This is because you have an original x from the original price for her car insurance from last year before the increase in the present year Combine the x 101 x6698 Then Divide by 101 on both sides X6632 Read the Question Wade s Jewelers is advertising a man s watch for 16875 The ad states that this is a 25 savings off the regular price Find the regular price of the watch Start with variable x x025x16875 0 Why are there two x This is because you have an original x from the original price for the watch before the x for savings on the original Combine the x 75x16875 Then Divide by 75 on both sides To check plug in x X225

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