Deck 2: B: Review and Applications of Algebra

Question 1

Solve for the unknown variable:

Answer 1

x = 3

Question 2

Solve: 3.1t + 145 = 10 + 7.6t

Answer 2

t = 30

Question 3

Evaluate

Answer 3

1.33

Question 4

Solve for the following pair of equations to three figure accuracy.

Question 5

Evaluate to six-figure accuracy:

Question 6

Evaluate to six-figure accuracy:

Question 7

Evaluate to six-figure accuracy:

Question 8

Solve for the unknown variable:

Question 9

Evaluate to six-figure accuracy:

Question 10

Solve: 1.25y - 20.5 = 0.5y - 11.5

Question 11

Simplify the following equation

Question 12

Evaluate: L(1 - d₁)(1 - d₂) for L = $1000, d₁ = 0.30, and d₂ = 0.20.

A) $440.00
B) $500.00
C) $1785.71
D) $560.00
E) $600.00

Question 13

Simplify:

Question 14

Evaluate to six-figure accuracy:

Question 15

Simplify:

Question 16

Use the formula V_f = V_i(1 + c₁)(1 + c₂)(1 + c₃) to determine c₂ if V_f = $586.64, _Vi = $500, c₁ = 0.17, and c₃ = 0.09.

Question 17

Solve the following pair of equations:

Question 18

Evaluate

Question 19

Evaluate to six-figure accuracy:

Question 20

Evaluate to six-figure accuracy:

Question 21

Solve for the following pair of equations to three figure accuracy

Question 22

Solve the following pair of equations. Verify your solution. g - h = 17

Question 23

Graph following equation: -2x + y = 4 over the range x = -3 to x = 6

Question 24

Solve the following pair of equations. Verify your solution. 318j - 451k = 7.22 -249j + 193k = -18.79

Question 25

Solve the following set of equations graphically:

Question 26

Solve the following pair of equations. Verify your solution. 4a - 3b = -3 5a - b = 10

Question 27

Evaluate the following:

Question 28

Graph following equations: y = 4 over the range x = -3 to x = 6

Question 29

Solve the following pair of equations. Verify your solution. 0.33e + 1.67f = 292 1.2e + 0.61f = 377

Question 30

Gamma Corp. manufactures and sells widgets for $6.00 each. Therefore, its total revenue, TR, from the sale of X widgets in a year is TR = $6X
It costs Gamma $2 for materials and labour to produce each widget. In addition, Gamma expects to incur $80,000 of other costs during a year. Therefore, Gamma's total costs for the year, TC, are expected to be
-720TC = $2X + $80,000
Gamma's expected net income, NI, for the year will be
NI = TR - TC
= $6X - ($2X + $80,000)
= $4X - $80,000
a) What is the slope and TR-intercept of a TR vs. X plot?
b) What is the slope and TC-intercept of a TC vs. X plot?
c) What is the slope and NI-intercept of an NI vs. X plot?
d) Which of the three plotted lines is steepest?
e) How much does NI increase for each widget sold?
f) If Gamma were able to reduce its materials and labour cost to $1.75 per widget, state for each plotted line whether its slope would increase, decrease, or remain unchanged.

Question 31

Solve for the unknown variable:

Question 32

Solve accurate to the cent:

Question 33

Solve the following set of equations graphically:

Question 34

Solve for the following pair of equations to three figure accuracy

Question 35

Solve the following set of equations graphically:

Question 36

Solve the following pair of equations.

Question 37

Solve the following set of equations graphically:

Question 38

Solve for the unknown variable:

Question 39

Solve for the following pair of equations to three figure accuracy

Question 40

Determine the slope and y-intercept of each of the following equations.
a) 2b + 3 = 5a
b) 3a - 4b = 12
c) 0 = 2400 - 4a - 5b
d) 7a = -89b

Question 41

Mrs. Simone invested $20,000 in two investments paying 2% and 3% respectively. She earned $460 interest for the year. How much did Mrs. Simone invest at 3%?

Question 42

Executive Fashions sold four-sevenths of its inventory at cost in a bankruptcy sale. The remainder was sold to liquidators for $6,700 representing 45% of the cost of the goods.
a) What was the original cost of the inventory that was sold to the liquidators?
b) What were the proceeds from the bankruptcy sale?

Question 43

The annual net income of the Todd Bros. partnership is distributed so that Ken receives $15,000 more than 80% of Hugh's share. How should a net income of $98,430 be divided between the partners?

Question 44

David's portfolio consists of bonds and equity. The bond market rose by 2.5%, while the equity market dropped by 10.5%. David's portfolio increased by 1.25%. What portion of bonds and equity did he have in his portfolio?

Question 45

During a one-day special, a grocery store sells cucumbers at 98 cents each or four for the price of three. At the end of the day, the store's computer reports that revenue from the sale of 541 cucumbers was $418.46. How many cucumbers were sold on the four-for-three promotion?

Question 46

Tickets for the end of semester dance sold for $10 if purchased in advance, and $15 if purchased at the door. If 392 tickets were sold for a total of $4280, how many tickets were sold at the door?

Question 47

TinyTot School purchases the same amount of milk and orange juice each week. After price increases from $1.10 to $1.15 per litre of milk and from $0.98 to $1.14 per can of frozen orange juice, the weekly bill rose from $42.20 to $45.85. How many litres of milk and cans of orange juice are purchased every week?

Question 48

Granola king wishes to mix raisins and granola together to create a cereal. Raisins are priced at $7.25 per Kg while granola is priced at $5.60. If the cereal is to be priced at $6.85 per Kg, then what is the appropriate mix of raisins and granola?

Question 49

Marika bought 5 litres of milk and 4 dozen eggs for $13.97. Lester purchased 9 litres of milk and 3 dozen eggs for $16.83. What were the prices for a litre of milk and a dozen eggs?

Question 50

Solve the following set of equations graphically:

Question 51

As a fundraiser, a local charity sold raffle tickets on a trip to Disney World at $2 each or three for $5. In all, 3,884 tickets were sold for a total of $6,925. How many people bought tickets at the three for $5 discount?

Question 52

Larissa works in a retail store in Square One in Mississauga. She earns a base salary of $320 per week, and a commission of 3% on sales over her quota of $5,000. If Larissa earned $515 last week, what was the value of her sales?

Question 53

A manufacturing firm pays monthly salaries of $3,400 to each production worker and $2,800 to each assembly worker. As the economy drops into a recession, the firm decides to reduce its total monthly manufacturing payroll from $253,800 to $198,000 by laying off 20% of its production workers and 25% of its assembly workers. How many layoffs will there be from each of the assembly and production divisions?

Question 54

Kristina is in charge of billing for a company that does computer training. She is preparing an invoice for $1,340 for 32 hours of work, which includes training at $70 per hour and preparation of a manual at $25 per hour. How many hours of training are included in the invoice?

Question 55

$100,000 is to be distributed under a firm's profit-sharing plan. Each of 3 managers is to receive 20% more than each of 26 production workers. How much will each manager and production worker receive?

Question 56

Solve the following set of equations graphically:

Question 57

Bart purchased 60% of a three-eighths interest in a ski chalet for $25,000. What was the implied value of the chalet?

Question 58

Sam earns $17.00 per hour for a forty-hour week. His overtime rate is 1 ½ times any hours exceeding forty in a week. If Sam earned $807.50 last week, how many overtime hours did he work?

Question 59

A convenience store sells canned soft drinks at $4.35 for a six-pack or 90 cents for a single can. If revenue from the sale of 225 cans of soft drinks on a weekend was $178.35, how many six-packs and how many single cans were sold?

Question 60

The Canucks charge $150 for Premium Tickets and $80 for Standard Tickets. If 18,500 tickets were sold for the Montreal game and $2,215,000 in revenues were recorded, how many Premium and Standard tickets were sold?

Question 61

What amount after a reduction of 25% equals $50?

Question 62

$754.30 is what percent less than $759.00?

Question 63

Tina drove from Calgary to Vancouver, a distance of 1,000 km, in 12.3 hours. She drove at 100 km/h on the "open road," but slowed to 50 km/h on urban and curving roads. What distance did she drive at each speed? (Hint: Travelling time at a particular speed is Distance/Speed)

Question 64

77,787 is what percent more than 77,400?

Question 65

How much is $56 increased by 65%?

Question 66

The Hungry Heifer diner offers an all-you-can-eat buffet at $12.95 per adult and $8.95 per child. On a particular day, the diner had total buffet revenue of $3,304.70 from 266 customers. How many of the customers were children?

Question 67

Shirley had a three-sevenths interest in a partnership. She sold three-fifths of her interest for $27,000.
a) What is the implied value of Shirley's remaining partnership interest?
b) What is the implied value of the entire partnership?

Question 68

Calculate the missing value: Initial Value = $100; Final Value = $95; Percent Change =?

Question 69

Calculate the missing value: Initial Value = 0.043; Final Value =?; Percent Change = -30%

Question 70

Calculate the missing value: Initial Value = 26.3cm; Final Value =?; Percent Change = 300%

Question 71

Calculate the missing value: Initial Value = 35kg; Final Value = 135kg; Percent Change =?

Question 72

What sum of money when increased by 7% equals $52.43?

Question 73

$1.5 million in bonus will be distributed to employees. Regular employees will each get an equal amount. Middle managers will get 2.5 times the regular employees bonus, while the executives get 5 times the bonus of middle managers. There are forty middle managers, 350 employees and 15 executives. Determine the bonus for regular employees, middle managers and executives.

Question 74

Dash Canada offers two long-distance telephone plans. Plan X costs 13 cents per minute for calls between 8 a.m. and 6 p.m. weekdays (business hours) and 9 cents per minute at other times. Plan Y costs 10.6 cents per minute any time. Above what percentage of business-hour usage will Plan Y be cheaper?

Question 75

A partnership in a public accounting practice has 7 partners and 12 accounting technicians. Each partner draws the same salary, and each technician is paid the same salary. The partners calculate that if they give the technicians a raise of 5% and if they increase their own salaries by 5%, the gross annual salaries for all accounting personnel will rise from the current $1,629,000 to $1,734,750. What are the current annual salaries of a partner and an accounting technician?

Question 76

Economy Truck Rentals offers short-term truck rentals consisting of an hourly rate plus a per-kilometre charge. Victor paid $39.81 for a two-hour rental during which he drove 47 km. Boyce paid $93.89 for five hours and 93 km driven. What rate did Budget charge per hour and per km?

Question 77

Mr. LeClair and Ms. Bartoli own adjacent hobby farms. They have just received their property tax bills for the current year. Mr. LeClair's property tax is $1,935 on a residence assessed at $200,000 and land with farm buildings assessed at $150,000. Ms. Bartoli's tax is $1,887 on her residence assessed at $175,000 and land with farm buildings assessed at $190,000. The regional government applies one tax rate to residences, and a lower tax rate to land with farm buildings. What are these property tax rates (expressed in percent to the nearest 0.01%)?

Question 78

José works in a toy manufacturing plant. The wooden toy he fabricates requires three steps: cutting, assembly, and painting. Assembly takes two minutes longer than half the cutting time, and painting requires half a minute longer than half the assembly time. How long does each step require if José made 72 units in 42 hours of work?

Question 79

Colby inherited a small savings-bond portfolio consisting of four $1,000 face-value Canada Savings Bonds and six $1,000 face-value Ontario Savings Bonds. In the first year, the portfolio earned $438 interest. At the end of the first year, Colby cashed in one of the Canada Savings Bonds and two of the Ontario Savings Bonds. In the following year, the remaining bonds earned $306 interest. What annual rate of interest did each type of bond earn?

Question 80

Buckerfields Garden Supply makes custom fertilizer by mixing appropriate combinations of bulk 6% nitrogen fertilizer with bulk 22% nitrogen fertilizer. How many kilograms of each type should be mixed to make 300 kg of 16% nitrogen fertilizer? (Hint: The weight of nitrogen in the mixture equals the total weight of nitrogen in the two components mixed together.)