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109.
Chapter 2
Solving Equations and Inequalities
Let x = number of investors. 240,000 240,000 = + 20,000 x x+2 240,000 240,000 + 20,000 x ( x + 2 ) x ( x + 2) = x x+2
(
)
(
)
240,000 ( x + 2 ) = 240,000 x + 20,000 x ( x + 2 ) 240,000 x + 480,000 = 240,000 x + 20,000 x 2 + 40,000 x 20,000 x + 40,000 x − 480,000 = 0 2
x 2 + 2 x − 24 = 0
( x + 6 )( x − 4 ) = 0 x+6=0
or
x−4=0
x = −6 ( x = −6 is not in the original domain.) There are 4 investors currently in the group. 110.
x=4
Let x = number of students. 1700 1700 = + 7.50 x x+6 1700 1700 x ( x + 6) + 7.50 x ( x + 6 ) = x x+6
(
)
(
)
1700 ( x + 6 ) = 1700 x + 7.50 x ( x + 6 )
1700 x + 10,200 = 1700 x + 7.5 x 2 + 45 x 7.5 x 2 + 45 x − 10,200 = 0 75 x 2 + 450 x − 102,000 = 0 3 x 2 + 18 x − 4080 = 0 x 2 + 6 x − 1360 = 0
( x + 40 )( x − 34 ) = 0 x + 40 = 0
x − 34 = 0
or
x = −40
x = 34
( x = −40 is not in the original domain.) There are 34 students currently in the group. 111.
Let x = average speed originally from Portland to Seattle. 145 145 12 = + x x + 40 60 1 145 145 5 x ( x + 40 ) + 5 x ( x + 40 ) = 40 5 x x +
(
)
725 x + 29000 = 725 x + x 2 + 40 x x 2 + 40 x − 29,000 = 0 Using the Quadratic Formula: x=
−40 ±
( 40 )
2
− 4 (1)( −29,000 )
2 (1)
−40 ± 117,600 ≈ 151.5 mi h 2 So, on the return trip from Seattle to Portland, the average speed is x + 40 = 191.5 mph. =
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Full file at https://testbankuniv.eu/College-Algebra-Real-Mathematics-Real-People-7th-Edition-Larson-Solutions-Manual