Deck 2: Equations and Inequalities

Question 1

Tell whether the number is a solution of the equation.

A) non-quantified solution
B) unequal solution
C) not a solution
D) solution
E) none of these

Answer 1

solution

Question 2

What number is 39% of 153? Round to two decimal places, if necessary.

A) 69.67
B) 5,967
C) 59.67
D) 159.67
E) 29.835

Answer 2

59.67

Question 3

What percent of 150 is 45?

A) 300%
B) 60%
C) 30%
D) 15%
E) 70%

Answer 3

30%

Question 4

Use the division or the multiplication property of equality to solve . What is the result? __________

Question 5

Is the statement below an expression or an equation? t = 3.85

A) an expression
B) an equation

Question 6

Use a property of equality to solve the equation. Then check the result. __________

Question 7

The state sales tax rate in Utah is 4.75%. Find the sales tax on a dining room set that sells for $1,100.00.

A) $1,047.75
B) $522.50
C) $5.23
D) $577.50
E) $52.25

Question 8

A smart phone is on sale for $180. If it has been marked down $75, find its regular price.

A) $75
B) $105
C) $180
D) $255
E) $13,500

Question 9

Solve the equation. Then check the result. h = _________

Question 10

Solve the equation. 4 s + 5 = 41

A) s = 17
B) s = 9
C) s = 4
D) s = 12
E) none of these

Question 11

Is the statement below an expression or an equation? t ² + 4.26 t = 7.6

A) an expression
B) an equation

Question 12

Use a property of equality to solve the equation. Then check the result. __________

Question 13

Tell whether the given number is a solution of the equation.

A) restricted solution
B) solution
C) not a solution
D) conflicting solution
E) none of these

Question 14

What number is of

A)
B)
C)
D)
E)

Question 15

Use an equation to solve the problem. A sport jacket that sells for $170 has a markup of $95. Find the wholesale price.

A) $55
B) $80
C) $90
D) $75
E) $65

Question 16

Use the division or the multiplication property of equality to solve . What is the result? __________

Question 17

Use an equation to solve the problem. A wholesale price for each compact disc is $14 and each has a markup of $0.70. Find the retail price of 40 CDs.

A) $532.00
B) $588.00
C) $560.00
D) $28.00
E) $392.00

Question 18

Tell whether the given number is a solution of the equation.

A) unqualified solution
B) removed solution
C) solution
D) not a solution
E) none of these

Question 19

Use the division or the multiplication property of equality to solve . What is the result?

A) 23
B) 24
C) 96
D) 97
E) 95

Question 20

An ________ is a statement indicating that two quantities are equal.

A) equation
B) expression

Question 21

Solve the formula for B . Volume of a pyramid:

A)
B)
C)
D)
E) none of these

Question 22

Solve the equation. 37 = -5 - 11 b

A)
B)
C)
D)
E)

Question 23

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 7 less than two-thirds of the number.

A) 21
B) 42
C) 35
D) 49
E) 28

Question 24

Solve A = P + Prt for A , given that P = $1100, , and t = 11 years.

A) A = $2,057.50
B) A = $2,007.50
C) A = $907.50
D) A = $2,307.50
E) A = $1,907.50

Question 25

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 34 inches. Find the length and width of the rectangle.

A) 6 inches wide, 11 inches long
B) 3 inches wide, 14 inches long
C) 4 inches wide, 13 inches long
D) 5 inches wide, 12 inches long
E) 8 inches wide, 9 inches long

Question 26

Solve the formula for the variable .

A)
B)
C)
D)
E)

Question 27

Use an algebraic approach to solve the problem: A board 35 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.

A) 35 feet
B) 7 feet
C) 21 feet
D) -7 feet
E) 14 feet

Question 28

The city's water department charges $8 per month, plus 44 cents for every 100 gallons of water used. Last month, one homeowner used 1,900 gallons and received a bill for $17.98. Was the billing correct? If the billing is not correct, what is the correct billing amount for this homeowner given these facts?

A) no; the billing amount is $15.59
B) yes; the billing amount is $17.98
C) no; the billing amount is $16.36
D) no; the billing amount is $15.38
E) none of these

Question 29

The perimeter of a rectangle with length and width is given by the formula . Solve this formula for . If the perimeter of a certain rectangle is 46.54 meters and its length is 16.25 meters, find its width.

A)
B)
C)
D)
E)

Question 30

The power lost when an electric current passes through a resistance is given by the formula . Solve for . If is 2,900 watts and is 16 amperes, calculate to the nearest hundredth of an ohm.

A)
B)
C)
D)
E)

Question 31

The masses of two objects are M₁ and M₂. The force of gravitation between the masses is given by where is a constant and is the distance between them. Solve for M ₂.

A)
B)
C)
D)
E)

Question 32

Solve the formula for the variable r . Then substitute numbers i = 56 , p = 100, and t = 7 to find the variable's value.

A) r = 37
B) r = - 51
C) r = 0.08
D) r = 163
E) r = 0.56

Question 33

Solve the formula for the variable .

A)
B)
C)
D)
E)

Question 34

Solve the equation. 2.8 = -10 t + 7.2

A) t = 7.44
B) t = 0.44
C) t = -0.56
D) t = 1.44
E) none of these

Question 35

Use an equation to solve the problem. A sport jacket that sells for $170 has a markup of $80. Find the wholesale price.

A) $70
B) $85
C) $75
D) $90
E) $100

Question 36

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $7,400. What was the average price of a home last year?

A) $89,500
B) $90,500
C) $93,500
D) $92,500
E) $88,500

Question 37

A call to Tucson from a pay phone in Chicago cost 85 cents for the first minute and 27 cents for each additional minute or portion of a minute. If a student has $9.00 in change, how long can she talk?

A) 42 min
B) 30 min
C) 34 min
D) 31 min
E) 38 min

Question 38

The illustration below is a schematic diagram of a resistor connected to a voltage source of 60 volts. As a result, the resistor dissipates power in the form of heat. The power P lost when a voltage V is placed across a resistance R is given by the formula If P is 12 watts and E is 60 volts, find R .

A) R = 300 ohms
B) R = 400 ohms
C) R = 250 ohms
D) R = 320 ohms

Question 39

Solve the formula for the variable .

A)
B)
C)
D)
E)

Question 40

Use an equation to solve the problem. Sales tax on a $11 compact disc is $0.55. At what rate is sales tax computed?

A) 9%
B) 5%
C) 4%
D) 8%
E) 6%

Question 41

The owner of a candy store wants to make a(n) 16-pound mixture of two candies to sell for $1 per pound. If red licorice bits sell for $0.90 per pound and lemon gumdrops sell for $1.30 per pound, how many pounds of each should be used? NOTE: All the values were rounded to the nearest whole number.

A) 4 lb. of lemon gumdrops, 12 lb. of red licorice bits.
B) 6 lb. of lemon gumdrops, 14 lb. of red licorice bits.
C) 8 lb. of lemon gumdrops, 6 lb. of red licorice bits.
D) 7 lb. of lemon gumdrops, 6 lb. of red licorice bits.
E) 5 lb. of lemon gumdrops, 15 lb. of red licorice bits.

Question 42

Paint costing $21 per gallon is to be mixed with 5 gallons of paint thinner costing $3 per gallon to make a paint that can be sold for $16 per gallon. Refer to the table below and compute how much of the new paint mixture will be produced. Paint gal Thinner gal Mixture gal

A) 21 gal
B) 14 gal
C) 19 gal
D) 20 gal
E) 18 gal

Question 43

Graph the solution set.

A)
B)
C)
D)
E)

Question 44

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal) of $4,450 has grown to be $4,720?

A) $260
B) $270
C) $255
D) $265
E) $290

Question 45

Two search-and-rescue teams leave base camp at the same time, looking for a lost child. The first team, on horseback, heads north at 2 mph, and the other team, on foot, heads south at 1 mph. How long will it take them to search a distance of 9 miles between them?

A) 5.5 hours
B) 3 hours
C) 4 hours
D) 3.5 hours
E) 4.5 hours

Question 46

If one of two supplementary angles is larger than the other, find the measure of the smaller angle.

A)
B)
C)
D)
E)

Question 47

Solve the inequality. Use interval notation to describe the solution.

A)
B)
C)
D)
E)

Question 48

Graph the solution set.

A)
B)
C)
D)
E)

Question 49

Lured by the ad in the illustration below, a woman invested $11,100, some in a money market account and the rest in a 5-year CD. How much was invested in each account if the income from both investments is $978 per year? First Republic Savings and Loan Account Rate NOW 5.5% Savings 7.5% Money market 8.0% Checking 4.0% 5-year CD 9.0%

A) $2,700 in the money market account, $8,400 in the CD
B) $1,900 in the money market account, $9,200 in the CD
C) $1,600 in the money market account, $9,500 in the CD
D) $1,800 in the money market account, $9,300 in the CD
E) $2,100 in the money market account, $9,000 in the CD

Question 50

An amount P , invested at a simple interest rate r , will grow to an amount A in t years, according to the formula A = P ( 1 + r t ). Suppose a man invested some money at 5.9%. If after 5 years, he had $6,151.25 on deposit, what amount did he originally invest? Round your answer to the nearest integer.

A) P = $4,900
B) P = $4,950
C) P = $4,750
D) P = $4,650

Question 51

A solution contains 0.2 liters of sulfuric acid. If this represents 8% of the total amount, find the total amount.

A) 3 liters
B) 3.5 liters
C) 1.5 liters
D) 5 liters
E) 2.5 liters

Question 52

At lunchtime, a man called his wife from his office to tell her that they needed to switch vehicles so that he could use the family van to pick up some building materials after work. The wife then left their home, traveling towards his office in their van at 32 mph. At the same time, the husband left his office in his car, traveling towards their home at 47 mph. If his office is 47.4 miles from their home, how long will it take them to meet so that they can switch vehicles?

A) 0.3 hr
B) 1.1 hr
C) 0.6 hr
D) 1.6 hr
E) 2.6 hr

Question 53

When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as and , are called adjacent angles. Angles that are nonadjacent, such as and or and , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If and , find x . Read as "the measure of ".

A) x = 11
B) x = 15
C) x = 6
D) x = 8
E) x = 10

Question 54

Find x .

A) x = 30
B) x = 37
C) x = 40
D) x = 32
E) x = 39

Question 55

Mary bought pound of two sorts of cookies for $1 per pound. If cookie with apricot jam $0.90 per pound and cookies with lemon jam $1.20 per pound, how many pounds of cookies with apricot jam did she buy? NOTE: Round your answer to the nearest tenth.

A) 0.7 lb. of cookies with apricot jam
B) 0.8 lb. of cookies with apricot jam
C) 0.5 lb. of cookies with apricot jam
D) 0.6 lb. of cookies with apricot jam
E) 0.9 lb. of cookies with apricot jam

Question 56

A garden store sells Kentucky bluegrass seed for $6 per pound and ryegrass seed for $3 per pound. How much rye must be mixed with 180 pounds of bluegrass to obtain a blend that will sell for $5 per pound?

A) 90 lb
B) 60 lb
C) 80 lb
D) 105 lb
E) 70 lb

Question 57

Granville and Preston are 522 miles apart. A car leaves Preston bound for Granville at 44 mph. At the same time, another car leaves Granville bound for Preston at 43 mph. How long will it take them to meet?

A) 7 hr
B) 6 hr
C) 3 hr
D) 5 hr
E) 4 hr

Question 58

Solve the inequality. Use interval notation to describe the solution.

A)
B)
C)
D)
E)

Question 59

Graph the inequality.

A)
B)
C)
D)
E)

Question 60

Cream is approximately 22% butterfat. How many gallons of cream must be mixed with milk testing at 2% butterfat to get 23 gallons of milk containing 6% butterfat? __________ gallons

Question 61

Solve the inequality. Give the result in interval notation. or

A)
B)
C)
D)
E)

Question 62

How long can a person rent the truck described in the ad if the cost is to be less than $120? Round your answer to the nearest hour.

A) Approximately 10 hr
B) Approximately 8 hr
C) Approximately 12 hr
D) Approximately 15 hr
E) Approximately 7 hr

Question 63

To hold the temperature of a room between and what Fahrenheit temperatures must be maintained?

A)
B)
C)
D)
E)

Question 64

Solve the problem by setting up and solving an appropriate inequality. Britney bowled 160 and 150 in her first two games. What must she bowl in the third game to have an average of at least 170 for the three games?

A)
B)
C)
D)
E)