Chapter 1 Preliminaries

1.2 Order of Operations

  • Simplify \(\$250 ( 1 + 0.065 × 172/365)\)
  • Simplify \(\$1775 ( 1 + 0.6/2)^3( 1 + 7.84/4)^2\)
  • Simplify \(\$1500/(1+ 0.08/12)^4\)
  • A hockey team says that its season ticket sales represent 72% of the stadium seating capacity of 18,500 seats. Rounded to the nearest 100, how many seats were not sold to season ticket holders?
  • Billy is a Realtor. He receives 44% of the 7% commission that the real estate agency charges on sales. If his sales for the past year were $14,500,000, what was the dollar value of his commission?

1.3 Rational Numbers

Simplify the following:

1.4 Expanding and Factoring

Simplify the following:

1.5 Solving Systems of Equations

Solve the following systems of equations by any method:

  • \(9x-6y = 18\) and \(2y = 2x - 2\)
  • \(2x - 2y = 2\) and \(6x + 8y = 40\)
  • \(x - y = 20\) and \((4/3)x + (5/2)y = 0\)
  • A car rental company charges an hourly rate plus a per kilometre charge. Jack paid $60 for a two-hour rental during which he drove 50 km. Jules paid $145 for five hours and 100 km driven. What rate is charged per hour and per kilometre?
  • Hank bought 8 steaks and 30 potatoes for $75. Kevin purchased 11 steaks and 20 potatoes for $75. What were the prices of the steak and potatoes.
  • A company pays monthly salaries of $5500 to each production worker and $4600 to each assembly worker. At the beginning of COVID, the firm decides to reduce its total monthly manufacturing payroll from $400,000 to $347,600 by laying off 20% of its production workers and 12% of its assembly workers. How many layoffs will there be from each of the assembly and production divisions?

1.6 Ratios, Proportions and Percentages

  • Solve the ratio \(165 : 245 = 65 : x\)
  • Solve the ratio \(1500: 2500 : 750 = x : 750 : y\)
  • Jim, Karen, and Sean started their partnership with a total investment of $245,000 contributed in the ratio of 4 : 6 : 3. If each partner contributes another $30,000, what will be the ratio of their total contributions? Leave your answer with the smallest term equal to 1.
  • The CPI was at 120 when the union signed their contract 5 years ago, the members of a union were earning $45.55 per hour. Now the current CPI at 135 and they want a new hourly rate that will restore their former purchasing power. What hourly rate are they seeking?
  • I live in a 4-plex. We need a new roof with costs totaling $35,000 and these costs must be divided between owners A, B, C, and D based on their square-footage 1300, 1400, 1750 and 2100 square feet, respectively. How much does each owner pay?
  • Jenny, Kathy, and Fred share the costs of their coffee fund in the ratio \(3/2 : 5/4 : 4/3\). How will costs of $50 be allocated among them?
  • Lisa receives a monthly base salary of $2500. On the first $15,000 of sales above her monthly quota of $25,000, she is paid a commission of 6%. On any additional sales, the commission rate is 10%. What were her total earnings for a month in which she had sales amounting to $45,000?
  • The price tags in Mel’s Flower Shop include the 8.25% tax. How much tax will she report for a plant sold at $49.55?
  • Okanagan Food-Mart usually spends half as much on radio advertising as on newspaper advertising, and 70% as much on television advertising as on radio advertising. If next year’s total advertising budget is $225,000, how much should be allocated to each form of advertising?
  • The government forecasts expenditure of $2.85 billion on education next year represents 21% of the provincial budget. Rounded to the nearest million dollars, what is the province’s total budget for the next year?