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Algebra 2
Solve a system of equations using substitution
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
A company that teaches self-improvement seminars is holding one of its seminars in Campbell. The company pays a flat fee of
$
208
\$208
$208
to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend
$
2
\$2
$2
to purchase books and supplies. Each attendee will pay
$
15
\$15
$15
for the seminar. Once a certain number of attendee register, the company will be breaking even. How many attendees will that take? What will be the company's total expenses and revenues?
\newline
Once
_
_
\_\_
__
attendees have registered, the company's expenses and receipts will both total
$
_
_
\$\_\_
$__
.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Mrs. Landry, the P.E. teacher, is pairing off students to race against each other. Patrick can run
4
meters per second
4\,\text{meters per second}
4
meters per second
, and Camille can run
5
meters per second
5\,\text{meters per second}
5
meters per second
. Mrs. Landry decides to give Patrick a head start of
26
meters
26\,\text{meters}
26
meters
since he runs more slowly. Once the students start running, Camille will quickly catch up to Patrick. How long will that take? How far will Camille have to run?
\newline
It will take
_
_
_
\_\_\_
___
seconds for Camille to run
_
_
_
\_\_\_
___
meters and catch up to Patrick.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
A fashion photographer needs to hire a stylist to prepare her models. Lacey charges
$
201
\$201
$201
for showing up, plus
$
71
\$71
$71
per hour. Cindy charges
$
198
\$198
$198
plus
$
74
\$74
$74
per hour. The photographer realizes that, given the expected duration of her photo shoot, either stylist would cost her the same amount. What would the duration be? What would the cost be?
\newline
If the shoot lasted for _____ hours, either stylist would cost
$
\$
$
_____.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Mrs. Sloan is a dance teacher whose students are going to have a recital. She is comparing two companies' prices for filming the recital and producing DVDs. Joy's Productions charges
$
4
\$4
$4
per DVD, plus
$
70
\$70
$70
to come and film the recital. Lanberry Media charges
$
79
\$79
$79
to film, plus
$
3
\$3
$3
per DVD. To decide which company to use, Mrs. Sloan determines the number of DVDs that would make the two options equivalent in terms of cost. How many DVDs would that be? How much would each option cost?
\newline
If Mrs. Sloan ordered _____ DVDs, the cost would be
$
\$
$
_____.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Sanjay, a caterer, is investing some money in equipment and employees to help grow his business. Recently he spent
$
98
\$98
$98
on equipment and hired a server who makes
$
13
\$13
$13
per hour. Sanjay is hoping to make up these expense at the next job that is scheduled, which pays a base of
$
95
\$95
$95
in addition to
$
14
\$14
$14
per hour that the server works. In theory, this event could pay enough to cancel out Sanjay's expenditures. How long would the job have to be? How much would the job pay?
\newline
If the job lasted _____ hours, the expenditures and pay would both be
$
\$
$
_____.
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Each big square below represents one whole. An array with
10
10
10
columns and
10
10
10
rows that represents
1
1
1
whole.
10
10
10
rows of
10
10
10
are shaded. An array with
10
10
10
columns and
10
10
10
rows that represents
1
1
1
whole.
10
10
10
rows of
10
10
10
are shaded. An array with
10
10
10
columns and
10
10
10
rows that represents
1
1
1
whole.
1
1
1
column of
10
10
10
is shaded.
1
1
1
column of
10
10
10
6
6
6
is shaded. An array with
10
10
10
columns and
10
10
10
rows that represents
1
1
1
whole.
1
1
1
column of
10
10
10
is shaded.
1
1
1
column of
10
10
10
6
6
6
is shaded. What percent is represented by the shaded area?
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c. Orange to total marbles
\newline
d. Orange, green and red to orange
\newline
5
:
15
5:15
5
:
15
\newline
8
,
2
:
8
:
5
8,2:8:5
8
,
2
:
8
:
5
\newline
Alexis is sharing Lifesavers candy. He is getting rid of all the grapes and keeping the cherry. His ratio from grape to cherry is
15
15
15
to
18
18
18
. If Alexis keeps the same ratio and gives his friend
5
5
5
grapes how many cherries should he share?
\newline
\newline
Grape
\newline
5
5
5
\newline
\newline
15
15
15
\newline
\newline
Cherry
\newline
\newline
18
18
18
\newline
\newline
\newline
Alexis Should Share
6
6
6
cherries with his friend
\newline
5
×
1.2
=
6
5\times1.2=6
5
×
1.2
=
6
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Solve the system of equations.
−
9
x
+
4
y
=
6
-9x + 4y = 6
−
9
x
+
4
y
=
6
and
9
x
+
5
y
=
−
33
9x + 5y = -33
9
x
+
5
y
=
−
33
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The ratio of new car sales to used car sales at the car lot is
3
:
5
3:5
3
:
5
. If the total car sales were
$
287
,
400
\$287,400
$287
,
400
last month, what was the total of the used car sales?
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A building contractor has a pickup truck with a rear storage area in the shape of a rectangular prism. The storage area has a length of
80
80
80
inches (in), a width of
60
60
60
i
n
\mathrm{in}
in
, and a height of
44
44
44
i
n
\mathrm{in}
in
. She wants to fill the entire storage area with equal-sized rectangular prism-shaped bricks with lengths of
8
8
8
i
n
\mathrm{in}
in
, widths of
4
4
4
i
n
\mathrm{in}
in
, and heights of
2
2
2
i
n
\mathrm{in}
in
. How many bricks can the contractor fit in the storage area of her truck?
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Steven and his cousin Carly are picking apples in their grandparents' orchard. Steven has filled
15
15
15
baskets with apples and is filling them at a rate of
4
4
4
baskets per hour. Carly has
11
11
11
full baskets and will continue picking at
8
8
8
baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How long will that take? How much fruit will they have picked by then?
\newline
In
_
_
_
\_\_\_
___
hours, the cousins will each have filled
_
_
_
\_\_\_
___
baskets with apples.
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Solve using substitution.
5
x
−
2
y
=
−
7
5x - 2y = -7
5
x
−
2
y
=
−
7
x
=
−
5
x = -5
x
=
−
5
(_,_)
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