Resources

Resources

Counting principle

Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by

b+2 c+3 j

b

is the number of hours Ben spends chopping,

c

is the number of hours Cam spends chopping, and

j

is the number of hours Justin spends chopping. How many trees do they chop down after Ben spends

8

hours chopping, Cam spends

3

hours chopping, and Justin spends

4

hours chopping?

Dominique is allowed to play up to

8

hours of video games this week. They want to play video games for at least

4

hours this weekend.

\newline

Which of the following can be used to represent

t

, the number of hours they can play video games before the weekend?

\newline

1

\newline

8-t \geq 4

\newline

8-t \leq 4

\newline

t-8 \geq 4

\newline

t-8 \leq 4

Kevin is playing a trivia game. The game awards the player

5

points for each correct answer, but deducts

2

points for each incorrect answer. If Kevin scores more than

100

points, which of the following describes

x

, the number of questions he answered correctly, and

y

, the number of questions he answered incorrectly?

\newline

1

\newline

2 x+5 y>100

\newline

5 x+2 y>100

\newline

2 x-5 y>100

\newline

5 x-2 y>100

Fabiano wants to score at least

6

5

points in a major chess tournament. He scores

1

point for each game that he wins, and he scores

0

5

points for each game that ends in a draw. Which of the following inequalities represents the number of games Fabiano should win

(W)

(D)

to achieve his goal?

\newline

1

\newline

W+0.5 D \leq 6.5

\newline

0.5 W+D \geq 6.5

\newline

W+0.5 D \geq 6.5

\newline

0.5 W+D \leq 6.5

At Andy's Market, the price of a box of brand-name cereal is

1

5

times the price of a box of generic cereal. If the price of a box of brand-name cereal is

\$ 3.60

, which of the following can be used to determine

x

, the price of a box of generic cereal in dollars?

\newline

1

\newline

\frac{x}{1.5}=3.6

\newline

1.5 x=3.6

\newline

3.6 x=1.5

\newline

x+1.5=3.6

Temperature can be measured in two different common units: degrees Celsius and degrees Fahrenheit.

\newline

f

represents the temperature in degrees Fahrenheit as a function of the temperature

c

in degrees Celsius.

\newline

f=32+1.8 c

\newline

Water freezes at

0

degrees Celsius. What is the freezing temperature of water in degrees Fahrenheit?

\newline

degrees Fahrenheit

Temperature can be measured in two different common units: degrees Celsius and degrees Fahrenheit.

\newline

f

represents the temperature in degrees Fahrenheit as a function of the temperature

c

in degrees Celsius.

\newline

f=32+1.8 c

\newline

What is the temperature increase in degrees Fahrenheit that is equivalent to a temperature increase by

10

degrees Celsius?

\newline

degrees Fahrenheit

The concession stand at a football game sells hot dogs and drinks. It costs

\$ 4.25

2

1

drink. It costs

\$ 7.00

3

2

drinks. Which of the following systems of equations can be solved to determine the cost,

h

, of each hot dog and the cost,

d

, of each drink?

\newline

1

\newline

2 h+d=7.00

\newline

3 h+2 d=4.25

\newline

2 h+d=4.25

\newline

3 h+2 d=7.00

\newline

3 h+d=7.00

\newline

2 h+2 d=4.25

\newline

2 h+2 d=4.25

\newline

2 h+d=7.00

Mikayla is the communications director for a politician and has recommended that a total of

41

speaking events are given by the politician before election day. Each speaking event is either a formal speech or an informal talk. Mikayla also recommends a total of

9

more formal speeches than informal talks. Which of the following systems of equations can be used to find out the number of formal speeches

s

versus the number of informal talks

t

\newline

1

\newline

t=s+9

\newline

s+t=41

\newline

t=s+9

\newline

s=t-41

\newline

s=t+9

\newline

s+t=41

S=40,000+500 c

\newline

Caden started a new job selling dental chairs. He earns a base salary plus a commission for every chair he sells. The given equation gives Caden's annual salary,

S

, in dollars, after selling

c

dental chairs. Based on the given equation, what is Caden's base salary?

\newline

1

\newline

\$ 39,500

\newline

\$ 40,000

\newline

\$ 40,500

\newline

\$ 50,000

For a high school dinner function for teachers and students, the math department bought

6

cases of juice and

1

case of bottled water for a total of

\$ 135

. The science department bought

4

cases of juice and

2

cases of bottled water for a total of

\$ 110

. How much did a case of juice cost?

\newline

1

\newline

\$ 12.50

\newline

\$ 15.00

\newline

\$ 20.00

\newline

\$ 25.00

Roberto plans to start a new job. In preparation, he decides that he should spend no more than

30

hours per week on the job and homework combined. If Roberto wants to have at least

2

homework hours for every

1

hour at his job, what is the maximum number of hours that he should spend at his job each week?

\newline

1

\newline

9

\newline

10

\newline

20

\newline

21

Prachi needs between

240

260

total feet of fence panels. The home improvement store has

24

6

-foot) fence panels and

28

8

-foot) fence panels in stock. Which of the following combinations of fence panels could she buy?

\newline

1

\newline

6

short fence panels and

26

long fence panels

\newline

8

short fence panels and

23

long fence panels

\newline

27

short fence panels and

12

long fence panels

\newline

30

short fence panels and

10

long fence panels