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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/XLX4L) _
WW % 30m ): 59%;) 2. If a 170pound person weighs approximately 65 pounds on
Mars, how much does a 9000pound satellite weigh? 170pound person on Earth = 65pound person on Mars
9000pound satellite on Earth xpound 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
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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»
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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)
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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.
 Fall '11
 JimCotter

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