Deck 4: Equations and Formulas

Question 1

Solve the equation.
g - 27.22 = 0

A)-26.22
B)26.22
C)-27.22
D)27.22

Answer 1

27.22

Question 2

Solve the proportion.

A)9
B)0.06
C)4.5
D)18

Answer 2

4.5

Question 3

Solve the problem.
Jim drove 117 miles in 3 hours. If he can keep the same pace, how long will it take him to drive 1,170 miles?

A)40 hr
B)351 hr
C)60 hr
D)30 hr

Answer 3

30 hr

Question 4

Provide an appropriate response.
Is this an application of the cross product method? If not, why not?

Question 5

A formula is given, along with values for all but one of the variables in the formula. Find the value of the variable that is not given. Round to the nearest hundredth when necessary.
P = 2L + 2w; P = 20, L = 7

A)L = 3
B)w = 13
C)w = 27
D)w = 3

Question 6

Provide an appropriate response.
Tell how you would split an amount according to a given ratio.

Question 7

Provide an appropriate response.
In the Multiplication Rule for solving equations, explain why each side of the equation must be multiplied or divided by the same nonzero number.

Question 8

A formula is given, along with values for all but one of the variables in the formula. Find the value of the variable that is not given. Round to the nearest hundredth when necessary.
d = rt; t = 5, d = 35

A)r = 40
B)r = 7
C)r = 30
D)d = 7

Question 9

Provide an appropriate response.
Explain how you would write a ratio in terms of whole numbers when one or both terms are fractions.

Question 10

Provide an appropriate response.
What is the cross product method? Use an example.

Question 11

Solve the equation.
m + 2.5 = 8.88

A)6.58
B)11.38
C)10.88
D)6.38

Question 12

Solve the equation.
4z + 19 = 3z + 2

A)-21
B)-17
C)21
D)17

Question 13

Determine if the proportion is true or false.

Question 14

Write the phrase as a mathematical expression. Use x as the variable.
Some number divided by 59

A)
B)59 - x
C)59x
D)59 + x

Question 15

Solve the equation.
-8 = b - 2

A)10
B)6
C)-10
D)-6

Question 16

A formula is given, along with values for all but one of the variables in the formula. Find the value of the variable that is not given. Round to the nearest hundredth when necessary.
C = 2 r; C = 31.40, = 3.14

A)r = 5
B)r = 34.54
C)r = 197.19
D)r = 10

Question 17

Solve the equation.
t - 3 = 18

A)21
B)-15
C)15
D)-21

Question 18

Provide an appropriate response.
Write a step-by-step explanation of how you would solve the equation for b.

Question 19

Provide an appropriate response.
In your own words, explain how you would solve a word problem using proportions.

Question 20

Solve the proportion.

A)0.04
B)7.14
C)24.5
D)8

Question 21

Solve the equation.

A)5
B)11
C)10
D)24

Question 22

Solve the equation.

A)11.5
B)31.5
C)30.5
D)12.5

Question 23

A formula is given, along with values for all but one of the variables in the formula. Find the value of the variable that is not given. Round to the nearest hundredth when necessary.
P = 4s; s = 33

A)s = 29
B)s = 132
C)P = 37
D)P = 132

Question 24

Solve the problem.
A woman invested $7,000 at 6% (or 0.06)for 7 years. How much did she have in her account at the end of 7 years?

A)$294
B)$9,940
C)$2,940
D)$5,880

Question 25

Solve the equation.
2.27x = 16.117

A)7.1
B)13.847
C)6.1
D)12.647

Question 26

Translate the statement into a mathematical expression.
Find the cost of 2 beds at b dollars each.

A)2 + b
B)2b
C)
D)2 - b

Question 27

Solve the formula for the specified variable.
S = for h

A)h = S - r
B)
C)
D)

Question 28

Solve the equation.
63 = 9k

A)53
B)6
C)7
D)54

Question 29

Determine if the proportion is true or false.

Question 30

Solve the problem.
Joan can mow a 3-acre field in 4 hours. How long would it take her to mow a 2.6-acre field? Round to the nearest tenth.

A)6.5 hr
B)5.5 hr
C)3.5 hr
D)0.9 hr

Question 31

Translate the statement into a mathematical expression.
An employee's salary, s, is increased by $290.

A)s - 290
B)290
C)s + 290
D)290s

Question 32

Write the phrase as a mathematical expression. Use x as the variable.
Some number multiplied by 5.98

A)5.98 - x
B)
C)5.98 + x
D)5.98x

Question 33

Solve the formula for the specified variable.
for n

A)
B)n = IR(Ir -E)
C)
D)

Question 34

Solve the problem.
Mara can type 56 words per minute. How many words would she type in hour (45 minutes)?

A)75 words
B)2,520 words
C)1,890 words
D)42 words

Question 35

Solve the equation.
-19 = 15 + f

A)4
B)34
C)-4
D)-34

Question 36

Solve the problem.
Stevie bought a stereo for $265 and put it on sale at his store at a 50% (or 0.5)markup rate. What was the retail price of the stereo?

A)$530.00
B)$397.50
C)$297.50
D)$365.00

Question 37

Solve the problem.
Dr. Taylor can see 11 patients in 2 hours. At this rate, how long would it take him to see 66 patients?

A)11 hr
B)22 hr
C)12 hr
D)363 hr

Question 38

Solve the problem.
On a map of the Fox River, 1 centimeter equals 7 kilometers. If a trail by the river is actually 23.8 kilometers long, what is the length of the river on the map?

A)5.4 cm
B)16.8 cm
C)3.4 cm
D)6.8 cm

Question 39

Solve the equation.
7.1m + 2m - m = 30.78

A)8.1
B)7.1
C)3.8
D)38

Question 40

Solve the equation.
-26.8 - k = 17.4

A)9.4
B)-9.4
C)-44.2
D)44.2

Question 41

Solve the equation.
4 = b + 1

A)-5
B)-3
C)5
D)3

Question 42

Solve the proportion.

A)11.424
B)0.1
C)9.5
D)31.6

Question 43

Solve the equation.
-9b + 9 + 7b = -3b + 14

A)14
B)-9
C)5
D)-14

Question 44

Write the phrase as a mathematical expression. Use x as the variable.
10 less than a number

A)x - (-10)
B)10
C)10 - x
D)x - 10

Question 45

Solve the equation.

A)2
B)
C)
D)3

Question 46

Solve the problem.
At a movie theater, 46 more people attended the early show than the late show. There were 324 people who saw the movie that night. How many people attended the late show?

A)139
B)185
C)370
D)278

Question 47

Solve the equation.
4n - 2 = 18

A)5
B)6
C)20
D)16

Question 48

Solve the equation.
2(x - 3)= 4(x - 14)

A)50
B)31
C)25
D)62

Question 49

Solve the formula for the specified variable.
a + b = s + r for s

A)
B)s = r(a + b)
C)s = a + b - r
D)

Question 50

Solve the problem.
A machine can fill 7,704 boxes of cereal in 0.9 hour. How many boxes of cereal can it fill per hour?

A)7,705 boxes
B)7,704 boxes
C)8,560 boxes
D)6,934 boxes

Question 51

Solve the equation.
10r + 7 = 57

A)40
B)44
C)1
D)5

Question 52

Solve the equation.
10y = 5y + 5 + 4y

A)-5
B)50
C)-50
D)5

Question 53

A formula is given, along with values for all but one of the variables in the formula. Find the value of the variable that is not given. Round to the nearest hundredth when necessary.

A)B = 8
B)B = 648
C)B = 24
D)B = 81

Question 54

Write the phrase as a mathematical expression. Use x as the variable.
The difference of some number and 7.9

A)7.9
B)x - 7.9
C)x + 7.9
D)7.9x

Question 55

Solve the problem.
On a map, the length of a nature-center trail is 8.9 centimeters. If the scale is 1 centimeter to 40 kilometers, what is the actual length of the trail?

A)356 km
B)712 km
C)360 km
D)357 km

Question 56

Solve the equation.
a - 2 = -7

A)9
B)-5
C)-9
D)5

Question 57

A formula is given, along with values for all but one of the variables in the formula. Find the value of the variable that is not given. Round to the nearest hundredth when necessary.

A)h = 240
B)h = 6
C)h = 62
D)h = 15.5

Question 58

Solve the equation.
13.2 = 3.3c

A)8.9
B)9.9
C)3
D)4

Question 59

Solve the problem.
A cashier has a total of 120 bills, made up of fives and tens. The total value of the money is $870. How many ten-dollar bills does the cashier have?

A)54
B)81
C)66
D)27

Question 60

Write the phrase as a mathematical expression. Use x as the variable.
Some number increased by 80

A)80
B)x - 80
C)x + 80
D)80x

Question 61

Solve the formula for the specified variable.

A)
B)
C)
D)

Question 62

A formula is given, along with values for all but one of the variables in the formula. Find the value of the variable that is not given. Round to the nearest hundredth when necessary.

A)A = 9.42
B)A = 29.58
C)A = 6.14
D)A = 28.26

Question 63

Solve the formula for the specified variable.

A)
B)
C)
D)

Question 64

Solve the equation.

A)92
B)10
C)7
D)90

Question 65

Solve the equation.
9x = 72

A)63
B)62
C)7
D)8

Question 66

Write the phrase as a mathematical expression. Use x as the variable.
148 fewer than some number

A)148
B)x - 148
C)x + 148
D)148x

Question 67

Solve the problem.
Four times a number added to 8 times the number equals 36. Find the number.

A)5
B)3
C)4.5
D)1

Question 68

Solve the equation.
g + 11.37 = 0

A)-11.37
B)12.37
C)-12.37
D)11.37

Question 69

Solve the equation.
m + 0.0281 = 0.0325

A)0.0044
B)0.0244
C)0.0606
D)0.0106

Question 70

Solve the problem.
If 3 times a number is added to -7, the result is 10 times the number. Find the number.

A)6
B)-1
C)1
D)-6

Question 71

Solve the formula for the specified variable.
for h

A)
B)
C)
D)

Question 72

Solve the problem.
At a garage sale, the most expensive item was marked $25.00 more than the cheapest item. The sum of the two items was $26.90. Find the cost of the least expensive item.

A)$3.80
B)$22.10
C)$1.90
D)$26.90

Question 73

Determine if the proportion is true or false.

Question 74

Solve the equation.

A)
B)3
C)9
D)6

Question 75

Translate the statement into a mathematical expression.
There were 75 men and women at a meeting. If m of them were men, how many were women?

A)75 + m
B)75 - m
C)
D)75m

Question 76

Solve the problem.
A label printer prints 9 pages of labels in 4.5 seconds. How long will it take to print 288 pages of labels?

A)146 sec
B)148 sec
C)147 sec
D)144 sec

Question 77

Solve the problem.
A woman has $2.70 in dimes and nickels. She has 6 more dimes than nickels. How many nickels does she have?

A)14
B)16
C)34
D)20

Question 78

Solve the problem.
Dr. Wong can see 9 patients in 3 hours. At this rate, how long would it take her to see 27 patients?

A)27 hr
B)8 hr
C)9 hr
D)81 hr

Question 79

Solve the problem.
If a spring stretches 0.6 meter when a 3-kilogram weight is attached to it, how much will it stretch when an 8-kilogram weight is attached to it?

A)1.6 m
B)0.6 m
C)4.6 m
D)3.6 m

Question 80

Solve the equation.
y - 1.2 = 2.3

A)3.5
B)1.1
C)3.3
D)1.3