6-109.
The diagram at right represents an acrobat’s sequence of
moves on a tightrope, where m represents the distance in
feet that she covers each time she does a leap.
a.
How long is each of her leaps? How can you tell?
[ m = 3 feet ]
m
m
1
5
m
1
4
CC2.0
Chapter6 b. Write and solve an equation to find the length of each leap.
[ m + 1 + 5 + 1 = m + m + 4 or m + 7 = 2m + 4 ; m = 3 feet ]
6-110to6-115
c. How long is the tightrope? [ 10 feet
]
6-110.
Solve the following equations using any method. Show your work and check your
solution.
a.
684
3x + 10 = 25
[ x=5 ]
b.
5(x 2) = 30
[ x=8 ]
c.
2x 9 = x + 7
[ x = 16 ]
Core Connections, Course 2
6-111.
Use the 5-D Process to solve the following problem. Write an expression to represent
each column of your table.
Yosemite Falls, the highest waterfall in the United States, is actually made up of three
smaller falls. The Lower Yosemite Falls is 355 feet shorter than the Middle Cascades
Falls. The Upper Yosemite Falls is 80 feet more than twice the Middle Cascades
Falls. If the entire set of waterfalls is 2425 feet long, how tall is each of the smaller
waterfalls? [ Lower = 320 feet = x 355 , Middle Cascades = 675 feet = x ,
Upper = 1430 feet = 80 + 2x ]
6-112.
6-111.
6-111.
6-113.
6-112.
6-112.
6-113.
6-114.
6-113.
6-115.
Evaluate the following expressions.
Use the 5-D Process to solve the following problem. Write an expression to represent
of your
+ 8 when
x = table.
9 [ 71 ]
a.each7xcolumn
b.
6(y 11) when y = 6 [ –102 ]
Falls,
highest
is an
actually
made
up]represent
of three
Use45
the 5m
5-D
tomsolve
problem.
expression
to
2tStates,
+Write
9 when
t = 20
+Process
7 the
c.Yosemite
when
= waterfall
4the[ following
72 ] in thed.United
[ 49
smaller
falls. of
The
Lower
each column
your
table.Yosemite Falls is 355 feet shorter than the Middle Cascades
Falls. The Upper Yosemite Falls is 80 feet more than twice the Middle Cascades
Falls.
If the
entire
set
of waterfalls
is 2425
long,
how tall
is each made
of theup
smaller
Yosemite
Falls,
highest
waterfall
the feet
United
States,
actually
of three
Here
are some
newthe
distances
with
giveninlengths
to help
Ceciliscross
the tightrope.
x
x
355
waterfalls?
[
Lower
=
320
feet
=
,
Middle
Cascades
=
675
feet
=
,
smaller
falls.
Lower
Fallsforiseach
355 feet
shorterWrite
than your
the Middle
Cascades
Find
at least
twoThe
ways
to getYosemite
Cecil across
situation.
solutions
in
Upper
= 1430
feetYosemite
= 80 + 2xFalls
] is 80 feet more than twice the Middle Cascades
Falls.
The
Upper
symbolic form. [ Answers vary. ]
Falls. If the entire set of waterfalls is 2425 feet long, how tall is each of the smaller
[ Lower =19320
Middle
Cascades
a.waterfalls?
Span of tightrope:
feetfeet = x 355 ,Given
lengths:
4, 5,=7675
feet feet = x ,
Upper
= +1430
feet+=580
[ 3(4)
7 , 2(7)
] + 2x ]
Evaluate the following expressions.
b. Span of tightrope: 25 feet
Given lengths: 3, 6, 7 feet
7x ++87 ,when
a. [ 6(3)
b.
6(y 11) when y = 6 [ –102 ]
4(7) x 3= ]9 [ 71 ]
Evaluate the following expressions.
2t + 9 5,when
t = 20 [ 49 ]
45 of5m
+ 7 when
= 4 [ 72 ] Given
d. lengths:
c.c. Span
tightrope:
23 m
feet
2, 9 feet
7x + 82 ,when
2(9) +x 5= ]9 [ 71 ]
a. [ 5(5)
b.
6(y 11) when y = 6 [ –102 ]
Here
are some
distances
crosst =
the 20
tightrope.
2t +Cecil
9 when
5m +new
7 when
c. 45
m = with
4 [given
72 ] lengths
d. to help
[ 49 ]
Find at least two ways to get Cecil across for each situation. Write your solutions in
Walter
walked
15.5
blocks from
his]house to work. It took him 35 minutes. What is
symbolic
form.
[ Answers
vary.
his rate in blocks per hour? [ 26.57 blocks/hour ]
Here are some new distances with given lengths to help Cecil cross the tightrope.
a. Span of tightrope: 19 feet
Given lengths: 4, 5, 7 feet
Find at least two ways to get Cecil across for each situation. Write your solutions in
[ 3(4) + 7 , 2(7) + 5 ]
symbolic form. [ Answers vary. ]
b. Span
tightrope:
Given
lengths:
3, 6,
feet
Jana’s
momof
gave
her $10025tofeet
shop for some new
school
clothes.
She7 is
at the store
a. Span of tightrope: 19 feet
Given lengths: 4, 5, 7 feet
and has[ 6(3)
picked
a pair3of] pants that cost $49.50. She wants to spend the rest of her
+ 7out
, 4(7)
[ 3(4) + 7 , 2(7) + 5 ]
6-112.
6-112.
6-113.
6-112.
6-113.
6-113.
6-114.
Upper
= 1430
feet = 80expressions.
+ 2x ]
Evaluate
the following
Yosemite Falls, the highest waterfall in the United States, is actually made up of three
+ 8 when
x = 9 Yosemite
a. 7xfalls.
[ 71 ]
b. feet6(y
11)than
when
= 6 [Cascades
–102 ]
smaller
The Lower
Falls is 355
shorter
the yMiddle
Falls. The Upper Yosemite Falls is 80 feet more than twice the Middle Cascades
Evaluate
expressions.
+ 9 tall
t = of20
5mfollowing
+ 7 when
c. 45
m = 4 [ is
722425
]
d. long,2thow
when
49 ]
Falls.
If the
the
entire
set of
waterfalls
feet
is each
the[smaller
waterfalls? [ Lower = 320 feet = x 355 , Middle Cascades = 675 feet = x ,
7x =+ 1430
8 when
9 +[ 2x
a.
71 ]]
b.
6(y 11) when y = 6 [ –102 ]
Upper
feetx==80
Here are some new distances with given lengths to help Cecil cross the tightrope.
2t + 9 when
t =your
20 solutions
5m +two
7 ways
c.Find45
when tomget
= Cecil
4 [ 72
]
[ 49 ] in
at least
across
ford.each situation.
Write
symbolic form. [ Answers vary. ]
Evaluate the following expressions.
Here
some
new distances
with given lengths
to help
Cecil 4,
cross
a. are
Span
of tightrope:
19 feet
Given
lengths:
5, 7the
feettightrope.
7x
+
8
x
=
9
a. at
when
[
71
]
b.
6(y
11)
when
y
= solutions
6 [ –102in]
Find
least
two
ways
to
get
Cecil
across
for
each
situation.
Write
your
[ 3(4) + 7 , 2(7) + 5 ]
symbolic form. [ Answers vary. ]
2t + 9 when
+ 7 when 25
c.b. 45
m =feet4 [ 72 ]
d.
Span5m
of tightrope:
Given lengths:
3, 6, t7=feet20 [ 49 ]
a. Span
of+tightrope:
Given lengths: 4, 5, 7 feet
[ 6(3)
7 , 4(7) 319] feet
[ 3(4) + 7 , 2(7) + 5 ]
c.
of tightrope:
23 feet
Given
lengths:
2, 9 the
feettightrope.
Here Span
are some
new distances
with given lengths
to help
Cecil5,cross
b.
Span
of
tightrope:
25
feet
Given
lengths:
3,
6,
7
feet
[
5(5)
2
,
2(9)
+
5
]
Find at least two ways to get Cecil across for each situation. Write your solutions in
[ 6(3)form.
+ 7 , 4(7)
3 ] vary. ]
symbolic
[ Answers
c.
Given
a. Span
Span of
of tightrope:
tightrope: 23
19 feet
feet
Givenlengths:
lengths: 5,
4,2,
5,97feet
feet
Walter
walked
15.5
blocks
from his house to work. It took him 35 minutes. What is
[[ 5(5)
2
,
2(9)
+
5
]
3(4) + 7 , 2(7) + 5 ]
his rate in blocks per hour? [ 26.57 blocks/hour ]
b.
Span of tightrope: 25 feet
Given lengths: 3, 6, 7 feet
[
6(3)
+
7
,
4(7)
3
]
6-114.
Walter walked 15.5 blocks from his house to work. It took him 35 minutes. What is
his
rate mom
in blocks
[to26.57
6-115.
gaveper
herhour?
$100
shop blocks/hour
for some Given
new] school
clothes.
c.Jana’s
Span of tightrope:
23 feet
lengths:
5, 2, 9She
feetis at the store
and [has
picked
out
a
pair
of
pants
that
cost
$49.50.
She
wants
to
spend
the rest of her
5(5) 2 , 2(9) + 5 ]
money buying various colors of a shirt that is on sale for $12.99. Write an inequality that can be used to calculate the number of shirts she can buy. Solve your inequality.
6-115.
Jana’s
mom gave
shop[ for
some+ new
school$100
clothes.
is .atShe
the can
storebuy
3.89
How many
shirtsher
can$100
Jana to
buy?
. s She
$49.50
$12.99s
and
has
picked
out
a
pair
of
pants
that
cost
$49.50.
She
wants
to
spend
the
rest
of her
6-114.
Walter
walked
15.5 blocks from his house to work. It took him 35 minutes. What
is
3 shirts.
]
money
buying
various
colors
of
a
shirt
that
is
on
sale
for
$12.99.
Write
an
inequality
his rate in blocks per hour? [ 26.57 blocks/hour ]
that can be used to calculate the number of shirts she can buy. Solve your inequality.
How many shirts can Jana buy? [ $49.50 + $12.99s $100 . s 3.89 . She can buy
3 shirts. ]
Chapter 6: Solving Inequalities and Equations
6-115.
Jana’s mom gave her $100 to shop for some new school clothes. She is at the store 685
and has picked out a pair of pants that cost $49.50. She wants to spend the rest of her
money buying various colors of a shirt that is on sale for $12.99. Write an inequality
that can be used to calculate the number of shirts she can buy. Solve your inequality.
Chapter 6: Solving Inequalities and Equations
685
How many shirts can Jana buy? [ $49.50 + $12.99s $100 . s 3.89 . She can buy
3 shirts. ]
Chapter 6: Solving Inequalities and Equations
685