Equations and Problem Solving

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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
(For help, go to Lesson 1-1.)
Write a variable expression for each
situation. 1. value in cents of q
quarters 2. twice the length 3. number of
miles traveled at 34 mi/h in h hours 4. weight
of 5 crates if each crate weighs x
kilograms 5. cost of n items at 3.99 per item
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
Solutions
1. value in cents of q quarters 25q 2. twice the
length 2 3. number of miles traveled at 34
mi/h in h hours 34h 4. weight of 5 crates if
each crate weighs x kilograms 5x 5. cost of n
items at 3.99 per item 3.99n
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
The width of a rectangle is 3 in. less than its
length. The perimeter of the rectangle is 26 in.
What is the width of the rectangle?
Relate The width is 3 in. less than the length.
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
(continued)
The width of the rectangle is 3 in. less than the
length, which is 8 in. So the width of the
rectangle is 5 in.
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
The sum of three consecutive integers is 72.
Find the integers.
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
(continued)
x x 1 x 2 72
3x 3 72 Combine like terms.
If x 23, then x 1 24, and x 2 25. The
three integers are 23, 24, and 25.
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
An airplane left an airport flying at 180 mi/h.
A jet that flies at 330 mi/h left 1 hour later.
The jet follows the same route as the airplane on
parallel altitudes. How many hours will it take
the jet to catch up with the airplane?
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
(continued)
180t 330(t 1) 180t 330t 330 Use the
Distributive Property.
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
Suppose you hike up a hill at 4 km/h. You hike
back down at 6 km/h. Your hiking trip took 3
hours. How long was your trip up the hill?
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
(continued)
4x 6(3 x)
4x 18 6x Use the Distributive Property.
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
Two jets leave Dallas at the same time and fly
in opposite directions. One is flying west 50
mi/h faster than the other. After 2 hours, they
are 2500 miles apart. Find the speed of each jet.
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
(continued)
4x 100 2500 Combine like terms.
4x 100 100 2500 100 Subtract 100 from
each side. 4x 2400 Simplify.
The jet flying east is flying at 600 mi/h. The
jet flying west is flying at 650 mi/h.
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Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
1. The sum of three consecutive integers is 117.
Find the integers. 2. You and your brother
started biking at noon from places that are 52 mi
apart. You rode toward each other and met at 200
p.m. Your brothers average speed was 4 mi/h
faster than your average speed. Find both
speeds. 3. Joan ran from her home to the lake at
8 mi/h. She ran back home at 6 mi/h. Her total
running time was 32 minutes. How much time did it
take Joan to run from her home to the lake?
38, 39, 40
your speed 11 mi/h brothers speed 15 mi/h
about 13.7 minutes
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