Deck 2: Equations, Inequalities, and Problem Solving

Question 1

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

Answer 1

6

Question 2

Use the division or the multiplication property of equality to solve the equation. $\frac { 12 } { 3 } = 6 x$

A)x = 6
B) $x = \frac { 1 } { 6 }$
C) $x = \frac { 2 } { 3 }$
D)x = 3

Answer 2

$x = \frac { 2 } { 3 }$

Question 3

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

Answer 3

73

Question 4

Tell whether the given number is a solution of the equation. $$8 k + 9 = 9 k - 1 ; k = 8$$

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

Question 5

Use the division or the multiplication property of equality to solve $\frac { v } { 6 } = 4$ . What is the result?

A)24
B)25
C)0.67
D)1.50
E)2.50

Question 6

Use the division or the multiplication property of equality to solve $13 = \frac { y } { 8 }$ . What is the result?

A)1
B)208
C)104
D)0.13
E)103

Question 7

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

Question 8

Solve the equation. 9( z + 2)= 36

A)z = 1
B)z = 13
C)z = 6
D)z = 2
E)z = 9

Question 9

Solve the equation. $$9 y - 30 + 15 y - 9 y + 45 = 120$$

A)y = 12
B)y = -7
C)y = 3
D)y = 7
E)y = 8

Question 10

Solve the equation. 6 x + 3 = 33

A)x = 8
B)x = 5
C)x = 4
D)x = 9
E)none of these

Question 11

Solve the equation. 6.5 = -10 t + 9

A)t = 2.25
B)t = 0.25
C)t = 0.250
D)t = 6.25
E)none of these

Question 12

Use the division or the multiplication property of equality to solve $3 x = 195$ . What is the result?

A)64
B)65
C)585
D)586
E)584

Question 13

Solve the equation. 45 = -2 - 13 y

A) $y = \frac { 47 } { 13 }$
B) $y = - \frac { 47 } { 13 }$
C) $y = - \frac { 43 } { 13 }$
D) $y = - \frac { 13 } { 47 }$
E) $y = \frac { 43 } { 13 }$

Question 14

Solve the equation. 5( t - 1)+ 2( t - 1)= -2( t - 2)+ 10( t + 2)

A)t = -37
B)t = -33
C)t = -31
D)t = -25
E)t = -28

Question 15

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

Question 16

Tell whether the given number is a solution of the equation. $$\frac { y } { 3 } = 5 ; y = 18$$

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

Question 17

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

Question 18

Tell whether the number is a solution of the equation. $$\frac { 2 + x } { 8 } - x = \frac { 1 } { 4 } ; x = 0$$

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

Question 19

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

Question 20

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

Question 21

To promote sales, a free 5-ounce bottle of shampoo is packaged with every large bottle (see illustration). Use the information on the package to determine how many ounces of shampoo the large bottle contains. __________ oz

Question 23

Find the number of gallons of sulfuric acid in 50 gallons of solution in a tank, if the percent of sulfuric acid is 50%.

A)25 gal
B)4.5 gal
C)9 gal
D)18 gal
E)50 gal

Question 24

An art gallery displays paintings for artists and receives a commission from the artist when a painting is sold. What is the commission rate if a gallery received $171.70 when a painting was sold for $1,010.00? __________ %

Question 25

Change 0.64 to a percent.

A)0.0064%
B)0.064%
C)6.4%
D)64%
E)none of these

Question 26

Solve the equation. $$\frac { 9 n } { 10 } - \frac { n } { 12 } = \frac { - 392 } { 60 }$$

A)n = -8
B)n = -14
C)n = 8
D)n = 10
E)n = -11

Question 27

Solve the equation. $$\frac { y } { 5 } + \frac { y - 102 } { 6 } = \frac { 3 y + 6 } { 3 }$$

A)y = -5
B)y = -6
C)y = -29
D)y = -32
E)y = -30

Question 29

$63$ is $33 \frac { 1 } { 3 } \%$ of what number?

A)94.5
B)1,890
C)567
D)189
E)378

Question 30

30 is what percent of 300?

A)2%
B)1%
C)20%
D)100%
E)10%

Question 31

After selling a house for $82,000, a real estate agent split the 6% commission with another agent. How much did each person receive? $__________

Question 32

What number is 77% of 100?

A)87
B)7,700
C)77
D)177
E)38.5

Question 33

Solve the equation. $$\frac { 3 a - 3 } { 6 } + \frac { 6 a - 6 } { 6 } + \frac { 4 a + 12 } { 8 } = 10$$

A)a = 10
B)a = -5
C)a = 2
D)a = 5
E)a = 8

Question 34

Solve the equation. If it is an identity or an impossible equation, so indicate. $$\frac { 5 ( x - 9 ) } { 10 } - \frac { - 75 x } { 50 } = \frac { 10 ( x + 11 ) } { 5 }$$

A)equation has one solution
B)identity equation
C)impossible equation

Question 35

If a woman making $30,000 a year receives a cost-of-living increase of 2.6%, how much is her raise? $__________

Question 36

Change the following percent to a decimal. 0.4%

A)40
B)0.0004
C)0.4
D)0.04
E)0.004

Question 37

Solve the equation. If it is an identity or an impossible equation, so indicate. 8 ( y - 7 )- y = 7 ( y - 8 )

A)impossible equation
B)identity equation
C)equation has one solution

Question 38

A salesperson for a medical supplies company is paid a commission of 6% for orders under $9,000. For orders exceeding $9,000, she receives an additional 1% in commission on the total amount. What is her commission on a sale of $12,300? $__________

Question 39

The cost to repair a car after a collision was $2,400. The automobile insurance policy paid the entire bill except for a $120 deductible, which the driver paid. What percent of the cost did he pay? __________ %

Question 40

Change 6 to a percent.

A)600%
B)0.06%
C)60%
D)0.6%
E)none of these

Question 41

Find three consecutive even numbers whose sum is 48.

A)7, 9, 11
B)14, 16, 18
C)-14, -12, -10
D)16, 18, 20
E)10, 13, 16

Question 42

After flooding damaged much of the crop, the cost of a head of lettuce jumped from $0.80 to $1.92. What percent of increase is this? __________ %

Question 43

Solve the formula $c = \frac { 1 } { 2 } ( B + t ) x$ for the variable $x$ .

A) $x = \frac { B + t } { 2 c }$
B) $x = \frac { c } { 2 ( B + t ) }$
C) $x = \frac { 2 ( B + t ) } { c }$
D) $x = \frac { 2 c } { B + t }$
E) $\chi = \frac { c } { 2 B + 2 t }$

Question 44

Complete the table by finding the simple interest earned. Principal Rate Time Interest earned $ 13000 8 % 3 yrs. ?

A)$31200
B)$312000
C)$3120
D)$31.2
E)$312

Question 45

Solve the formula $V = 6 ( r - 1 ) b$ for the variable $r$ .

A) $r = \frac { 6 \mathrm {~V} } { b } - 1$
B) $r = \frac { V + 1 } { 6 b }$
C) $= \frac { V } { 6 b } - 1$
D) $r = \frac { 6 \mathrm {~V} } { b } + 1$
E) $r = \frac { V } { 6 b } + 1$

Question 46

In an isosceles triangle, two sides are four times the length of the third side. Find the length of the SHORTEST side if the perimeter is 54 feet.

A)9 feet
B)8 feet
C)6 feet
D)5 feet

Question 47

Use an algebraic approach to solve the problem. Find three consecutive integers whose sum is 33.

A)-10, -11, -12
B)10, 9, 8
C)12, 13, 14
D)15, 16, 17
E)10, 11, 12

Question 48

Find the area of the circle to the nearest tenth, if and a = 3 in. __________ in

Question 49

Find the perimeter of the figure if $$a = 12 \mathrm { in } .$$

A)144 in.
B)12 in.
C)24 in.
D)48 in.
E)288 in.

Question 50

A 18-inch board has been cut into 2 sections, one 8 inches longer than the other. How long is the shorter piece.

A)5 inches
B)4 inches
C)7 inches
D)6 inches

Question 51

If one of two supplementary angles is $38 ^ { \circ }$ larger than the other, find the measure of the smaller angle.

A) $65.5 ^ { \circ }$
B) $74 ^ { \circ }$
C) $79.5 ^ { \circ }$
D) $71 ^ { \circ }$
E) $68 ^ { \circ }$

Question 52

A jewelry store buys pairs of earrings for $114 each and marks them up $17. What is the retail price of a pair of earrings? $__________

Question 53

A cattle rancher is going to sell one of his prize bulls at an auction and would like to make $46500 after paying a 7% commission to the auctioneer. For what selling price will the rancher make this amount of money?

A)$49,755
B)$50,000
C)$50,555
D)$55,000

Question 54

Complete the financial statement shown in the table. Quarterly Financials Income statement (dollar amounts in millions)Quarter ending Mar 00 Quarter ending Dec 99 Revenue $1,323.80 $1,513.20 Cost of goods sold $460.20 $780.70 Gross profit ? ?

A)Gross profit $863.60 $732.50
B)Gross profit $1,784.00 $2,293.90
C)Gross profit $873.80 $722.30

Question 55

The host of a TV infomercial says that the suggested retail price of a rotisserie grill is $40.00 and that it is now offered "for just 4 easy payments of only $6.30." What is the discount rate? __________ %

Question 56

A person has a temperature of $102 ^ { \circ } \mathrm { F }$ . What is the person's temperature, to the nearest tenth, on the Celsius scale?

A) $37.9 ^ { \circ } \mathrm { C }$
B) $36.9 ^ { \circ } \mathrm { C }$
C) $37.4 ^ { \circ } \mathrm { C }$
D) $38.4 ^ { \circ } \mathrm { C }$
E) $38.9 ^ { \circ } \mathrm { C }$

Question 57

The Great Pyramid at Giza in northern Egypt is one of the most famous works of architecture in the world. Use information in the illustration to find the volume to the nearest cubic foot. a = 455, b = 755 __________ ft

Question 58

Find the largest of three consecutive whole numbers such that twice the sum of the two smallest numbers is 12 more than three times the largest number.

A)20
B)16
C)17
D)19
E)18

Question 59

Convert $50 ^ { \circ } \mathrm { C }$ to degrees Fahrenheit.

A) $117 ^ { \circ } \mathrm { F }$
B) $122 ^ { \circ } \mathrm { F }$
C) $113 ^ { \circ } \mathrm { F }$
D) $482 ^ { \circ } \mathrm { F }$
E) $90 ^ { \circ } \mathrm { F }$

Question 60

Solve the formula $H = P T$ for the variable $T$ .

A) $T = \frac { P } { H }$
B) $T = H P$
C) $T = \frac { H } { P }$
D) $\frac { 1 } { T } = \frac { H } { P }$
E) $T = \frac { 1 } { H P }$

Question 61

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 62

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 63

What numbers satisfy the condition: six more than twice a number is at most 8?

A) $x \geq 1$
B) $x < 1$
C) $x > 1$
D) $x \leq 1$

Question 64

Tell whether the given number is a solution of the inequality. $3 x + 7 < 4 x - 2$ x = 13

A)yes
B)no

Question 65

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 66

When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as $\angle 1$ and $\angle 2$ , are called adjacent angles. Angles that are nonadjacent, such as $\angle 1$ and $\angle 3$ or $\angle 2$ and $\angle 4$ , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ and $m ( \angle 3 ) = ( 7 x - 10 ) ^ { \circ }$ , find x . Read $m ( \angle 1 )$ as "the measure of $\angle 1$ ".

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

Question 67

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 68

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 69

Find x .

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

Question 70

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 71

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. $p \cdot n = v$ Paint $\$ 21$ $x$ gal $\$ 21 x$ Thinner $\$ 3$ $5$ gal $\$ 3 ( 5 )$ Mixture $\$16$ $( x + 5 )$ gal $\$ 16 ( x + 5 )$

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

Question 72

Mary bought pound of two sorts of cookies for $1 per pound. If cookies 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 73

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 74

A student working for a delivery company earns $81.25 per day plus $4.75 for each package she delivers. How many deliveries must she make each day to earn $200 a day?

A)27 deliveries
B)25 deliveries
C)26 deliveries
D)22 deliveries
E)21 deliveries

Question 75

Determine which of the following is a solution of $- 2 x + 3 < - 1$ .

A)0
B)1
C)3
D)2

Question 76

A group of junior high students will be touring Washington, D.C. Their chaperons will have the $1,810 cost of the tour reduced by $15.50 for each student they personally supervise. How many students will a chaperon have to supervise so that his or her cost to take the tour will be $1,500?

A)17 students
B)16 students
C)22 students
D)19 students
E)20 students

Question 77

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 78

To help move his furniture, a man rents a truck for $38.00 per day plus 35 cents per mile. If he has budgeted $150 for transportation expenses, how many miles will he be able to drive the truck if the move takes 1 day?

A)320 miles
B)330 miles
C)305 miles
D)340 miles
E)325 miles

Question 79

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 80

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