7.6 - 7.6 Proportions and Problem Solving with Rational...

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Unformatted text preview: 7.6 Proportions and Problem Solving with Rational Eguations A ratio is the quotient of two numbers or two quantities. The ratio of the numbers a and b can also be written as cub, or The units associated with the ratio are important. The units should match. If the units do not match, it is called a rate, rather than a ratio. A proportio is two ratios (or rates) that are equal to each other. a = C We can rewrite the proportion by multiplying by the LCD, bd. This simplifies the pr0portion to ad = bc. This‘is commonly referred to as the cross product. 1. Solve the proportion for x. x+1__5 x+2_3 LCD : 309a) 30H. [x—z—l) :i/XLX4-L) _ WW % 30m ): 59%;) 2. If a 170-pound person weighs approximately 65 pounds on Mars, how much does a 9000-pound satellite weigh? 170-pound person on Earth = 65-pound person on Mars 9000-pound satellite on Earth x-pound satellite on Mars IQ—O ‘ 66-“ EVE—.2: @6730 . 9000 % 170K 2‘ 5—357)” 55“ x In similar triangles, the measures of corresponding angles are equal, and corresponding sides are in proportion. Given information about two similar triangles, you can often set up a proportion that will allow you to solve for the missing lengths of sides. 3. Given the following similar triangles, find the unknown length y. 12:»- _____ lo “‘ 12 m 5 m 10 m y Mada/L‘s l X fl. X 4. The quotient of a number and 9 times its reciproca 1. Find the number. __'_ ._L_::~ x,9x l 3&1 _)<_g—.€L:i 3 I X 3&3 3.22.:1 \ I 9 ,3.}-fl_ 2 *3 Lzl «sen—3 5. An experienced roofer can roof a house in 26 hours. A beginner needs 39 hours to do the same job. How long will it take if the two roofers work together? X hOwr5 =1/the time to do the job. Examgle: If it takes Shours to finish a job the work rate is 1/5 If it takes 3hours to finish a job the work rate is 1/3 In general: If it takes x hours to finish a job the work rate is 1/x 3 3. :4» fi’* “4% X __6_“__ - .37 6‘X:?‘8 #8 X: 3H? E 6’ g : l6'éla0wrs W9- fii— but _L ; fir, Li '5 X ail—it- :J’ 9x110 X 20920 I x:a.aA0M5 6. The speed of Lazy River’s current is 5 mph. A boat travels 20 miles downstream in the@ as traveling 10 miles upstream. Find the Speed of the boat in still water. 3 Distance 6 time = d/r Down 20 r + 5 20/(r + 5) Up 10 r—S 10/(r—5) de‘lvacQZ . +{rmL , dds'l— -— Hm __ SPQJLCL . 32.. ‘0 ,r mb’Xl“ 5’ r_ ash-*7) : ) p @ ZOYa_[U_D:lOV—l‘L7r—O 10w 7* [50 (a; , c3 6 X 5 .L. ___,__+ 1 .1. 6 E X “LL 3 ..L_ g X W '5- Q X : 6 1 {ma L f. {\LL ‘9 fH/y $IS+§VVUZ— Fifi m (a 42: X X ;g 18 )(+I .12: a: L63 X X4”! We BULQS‘fEUn I‘S [ZUWO : F3 Y age; for Au lszz” 13X @016 KHZ Dim r vel'nd m’h‘m ?@ [2: [9X fawn Owd 7560 m mt: (exode " ...
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This note was uploaded on 01/16/2012 for the course MATH 096 taught by Professor Jimcotter during the Fall '11 term at Truckee Meadows Community College.

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7.6 - 7.6 Proportions and Problem Solving with Rational...

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