Exam 2: Review and Applications of Algebra

In his sales job, Ehud earns a base salary of $1500 per month plus a commission of 5% on sales revenue. Write an equation for calculating his gross earnings, E, for a month in terms of his sales revenue, R. If you were to plot a graph of E vs. R, what would be the slope and E-intercept of the line?

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

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?

Solve: 5(2 - c) = 10(2c - 4) - 6(3c + 1)

Solve the following set of equations graphically: x = -y - 4 y = -5x - 4

Simplify and collect like terms: $\frac{x}{2}-x^{2}+\frac{4}{5}-0.2 x^{2}-\frac{4}{5} x+\frac{1}{2}$

A loan company dropped the interest rate it charges on second mortgages from 8.7% to 7.3%. What percent reduction did this represent?

Solve: 12x - 4(2x - 1) = 6(x + 1) - 3

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.

In 2016, Canada's population reached 32,500,000, a level that was 9.53% higher than ten years earlier. Rounded to the nearest 10,000, what was the population figure for 2006?

Simplify: $P\left(1+0.095 \times \frac{135}{365}\right)+\frac{2 P}{\left(1+0.095 \times \frac{75}{365}\right)}$

Evaluate and calculate to the cent: P(1 + i)ⁿ for P = $1,280, i = 0.025, n = 3

Calculate the missing value: Initial Value = 112g; Final Value =?; Percent Change = 112%

A car dealership's list price on cars is 18% above cost. Recently a demo was sold for $21,000, which is 15% off the list price. Determine the cost of the demo vehicle.

Perform the operation indicated and collect like terms: 5(2x - y)(y + 3x) - 6x(x - 5y)

The Euro is 8% greater than the US Dollar. By what percentage is the US Dollar less than the Euro?

Solve for the unknown variable: 9x + 10 = -3x + 34

Mutual Fund A charges an annual management fee of 2.38% of money under management. The corresponding management fee for Mutual Fund B is 1.65%. On the same invested amount, what percentage more fees will you pay to Fund A than to Fund B?

The formula for converting from Celsius temperatures, C, to Fahrenheit temperatures, F, is F = $\frac{9}{5}$ C + 32. a) If you were to plot a graph of F vs. C, what would be the slope and F-intercept of the line? b) The slope represents the change in F per unit change in C. Use the value of the slope to determine the increase in Fahrenheit temperature corresponding to a 10 Celsius-degree rise. c) Rearrange the given formula to obtain a formula for converting from Fahrenheit temperatures to Celsius temperatures. What would be the slope and C-intercept if C vs. F were plotted on a graph?

$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.