Deck 6: Topics in Algebra

Question 1

Answer 1

Question 2

The product of two consecutive positive even integers is 120. Find the integers.

Answer 2

10 and 12

Question 3

Answer 3

Question 4

Question 5

Solve the inequality:

Question 6

Solve:

Question 7

Question 8

Question 9

Solve:

Question 10

Question 11

The larger of two numbers is 3 more than the smaller number. The sum of the numbers is 21. Find the numbers.

Question 12

The difference of two numbers is 1. The sum of the numbers is 39. Find the numbers.

Question 13

Question 14

Write in symbols: The quotient of a number and 2.

Question 15

Question 16

Write the ratio as a fraction and reduce to lowest terms. 3 to 7

Question 17

Question 18

Write in symbols: 7 less than a number.

Question 19

Question 20

A couple has $20,000 to use toward the purchase their first home. If they put down a 20% down payment and pay $5,000 in closing costs, what is the maximum home price they can afford?

Question 21

Question 22

Determine whether the given value is a solution to the equation.
$$3 ( x + 1 ) ^ { 2 } = 48 ; x = 3$$

A) Yes
B) No

Question 23

Question 24

$$\text { Solve the equation. } - 2 x + 6 = 2$$

A) {2}
B) {-4}
C) {-7}
D) {5}

Question 25

A 3-foot pole casts a shadow of 8 feet. How tall is a tree with a shadow of 19 feet?

Question 26

Write in symbols: A number increased by 9.

Question 27

A math class containing 88 students was divided into two sections. One section has four more students than the other. How many students were in each section?

Question 28

Question 29

Question 30

At a certain restaurant, one out of every 7 customers orders a hamburger. If the restaurant has 126 customers in one day, how many hamburgers will they sell?

A) 20 hamburgers
B) 18 hamburgers
C) 19 hamburgers
D) 17 hamburgers

Question 31

Write the ratio as a fraction and reduce to lowest terms. 10 cents to 35 cents

Question 32

Three times a number is 10 less than five times the number. Find the number.

Question 33

Determine whether the given value is a solution to the equation.
$$- 5 ( x + 4 ) = - 3 x ; x = - 4$$

A) Yes
B) No

Question 34

Question 35

Question 36

$$\text { Solve: } - 8 x = 16$$

A) {8}
B) {-8}
C) {-2}
D) {2}

Question 37

A basketball team played 48 games and won 6 more games than it lost. Find the number of games the team won.

A) 15 games
B) 21 games
C) 27 games
D) 24 games

Question 38

Write the ratio as a fraction and reduce to lowest terms. 24:18

Question 39

$$\text { Evaluate: } - 3 x ^ { 2 } - 4 y ^ { 2 } + 2 x \text { when } x = - 5 \text { and } y = 2$$

A) -101
B) -81
C) -69
D) 49

Question 40

If the perimeter of a triangular flower bed is 13 feet with two sides the same length and the third side 4 feet longer, what are the measures of the three sides of the flower bed?

Question 41

How long will it take an object to hit the ground if it is dropped from a height of 1024 feet? (Use $d = r t + 16 t ^ { 2 }$ .) Assume the object initially is held still.

A) 8 sec
B) 4 sec
C) 16 sec
D) 32 sec

Question 42

The heat energy from electricity is given by the formula $E = 0.238 I ^ { 2 } R t$ . Find $E$ when $I = 50 \mathrm { amps } , R = 19 \mathrm { ohms }$ , and $t = 100 \mathrm {~s}$ . Round answer to the nearest hundredth.

A) 1,243,550.00
B) 1,130,500.00
C) 1,017,450.00
D) 22,610.00

Question 43

A community college has 3,000 students and 90 instructors. The college plans that enrollment will be 3,500 next year. How many new instructors should be hired if the college wants to keep the same student to instructor ratio?

A) 13 instructors
B) 77 instructors
C) 105 instructors
D) 15 instructors

Question 44

$$\text { The formula for the average } a \text { of two numbers } n \text { and } s \text { is } a = \frac { n + s } { 2 } \text {. Solve for } s \text {. }$$

A) a + 2 + n
B) 2a + n
C) 2a - n
D) a + 2 - n

Question 45

Question 46

Write the phrase in symbols: Eight less than three times a number.

Question 47

$$\text { Solve: } - 7 + x = - 6$$

A) {1}
B) {13}
C) {-1}
D) {-13}

Question 48

Steve earned scores of 84 and 75 on his first two exams. What will his average grade be if he gets a 78 on his third exam?

A) 84
B) 78
C) 79
D) 75

Question 49

Question 50

Write the ratio as a fraction and reduce to lowest terms. 4 feet to 20 inches

Question 51

A bus leaves from campus headed east at 25 miles per hour and another bus leaves from campus headed south at 35 miles per hour. How long will it take for the buses to be 172 miles apart? Round answer to the nearest hour.

A) 4 hours
B) 3 hours
C) 2 hours
D) 8 hours

Question 52

$$\text { Evaluate the formula } P = 2 l + 2 w \text { when } l = 7 \text { in. and } w = 5 \text { in. }$$

A) 12 in.
B) 24 in.
C) 19 in.
D) 17 in.

Question 53

Question 54

Question 55

Question 56

Question 57

Use the formula F = ma to solve. Find the acceleration for a force F = 585 newtons and a mass of 45 kg.

Question 58

Question 59

$$\text { Evaluate: } - 4 x - 2 \text { when } x = 1$$

A) 8
B) -2
C) -6
D) 2

Question 60

Question 61

A person sold their house for $100,000 and made a profit of 35%. How much did they pay for their home?

A) $66,666.66
B) $135,000.00
C) $74,074.07
D) $81,481.48

Question 62

Question 63

Question 64

An arithmetic student needs at least a 70% average to receive credit for the course. If she scored 85%, 79%, and 69% on the first three exams, what is the lowest score she can get on the fourth exam to receive credit for the course?

A) 47%
B) 49%
C) 45%
D) 52%

Question 65

The time to complete a project is inversely proportional to the number of people who are working on the project. A class project can be completed by 3 students in 24 days. In order to finish the project in 6 days, how many more students should the group add?

A) 15 more students
B) 12 more students
C) 18 more students
D) 9 more students

Question 66

A person drives 5,000 miles in 6 months. How many miles will that person drive in 3 years?

A) 2,500 miles
B) 90,000 miles
C) 30,000 miles
D) 10,000 miles

Question 67

The simple interest (I) on a certain amount of money (p) that is invested at a specified interest rate (r) for a specific period of time (t) can be found by the formula I = prt. Find the interest on a principal of $100 invested at 3% yearly for 7 years.

A) $21.00
B) $2100
C) $18.90
D) $1890.00

Question 68

State whether the equation is a linear equation in one variable or not.
$$2 x = 7 ( x - 2 )$$

A) Linear
B) Not linear

Question 69

$$\text { Evaluate the formula } F V = P ( 1 + r ) ^ { n } \text { when } P = \$ 100,000 , r = 0.08 \text {, and } n = 9$$

A) $249,875.58
B) $199,900.46
C) $179,910.41
D) $219,890.51

Question 70

Question 71

Solve by factoring.
$\frac { 1 } { 5 } x ^ { 2 } + \frac { 14 } { 5 } x + 9 = 0$

A) {-5, 9}
B) {5, 9}
C) {5, -9}
D) {-5, -9}

Question 72

If everyone had the same body proportions, your weight in pounds would vary directly with the cube of your height in feet. Assume the average height and weight of a female in your math class is 5'5" and 125 pounds. Use this information to write a variation equation then use it to find the weight of the female below if they had the same body type as the average female. Round answer to the nearest pound. Kelly 5'3"

A) 121 lb
B) 114 lb
C) 109 lb
D) 120 lb

Question 73

Question 74

Question 75

Simplify: -18a + 14a + 15a.

A) -19a
B) 47a
C) -17a
D) 11a

Question 76

Question 77

Question 78

Gail is trying to stay between 400 calories and 600 calories for lunch. She selects a sandwich for 150 calories and a salad for 50 calories. How many calories can she have for dessert?

A) Between 200 and 425 calories
B) Between 200 and 400 calories
C) Between 175 and 400 calories
D) Between 175 and 425 calories

Question 79

Question 80

Under certain conditions, the pressure of gas varies inversely with its volume. If a gas with a volume of 150 cubic inches has 29 pounds of pressure, find the amount of pressure 145 cubic inches of gas is under.