Exam 2: Review and Applications of Algebra

Simplify: $\frac{6 a+9}{3}-4(a-1)$

The Vancouver Real Estate Board stated that the average house price was $405,000 this year; an 8% increase over the same time last year. Determine the average house price last year.

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?

Evaluate the following: $\frac{1.04^{10}-1}{0.04}$

Goldfield Resources' share price fell by $4 in Year 1 and then rose by $4 in Year 2. If the share price was $6 at the end of Year 1, what was the percent change in share price each year?

Simplify the following: (a²) (a^-6) (a³)

Solve for x and y in the following pair of equations: y = -0.2x + 4.2 X - 0.5y = 10

When x is 3, the result of 5x³ + 7x² -30 is 127.

The statistics for a professional accounting program indicate that five-sevenths of those who enter the program complete Level 1. Two-ninths of Level 1 completers do not finish Level 2. If 587 students completed Level 2 last year, how many (including this group of 587) began Level 1?

In January of 2008, the federal government reduced the GST rate from 6% to 5%. What was the resulting percent reduction in the dollar amount of GST consumers paid on any item?

Simplify: h⁷ /h^-4

Erin has invested in both an equity mutual fund and a bond mutual fund. Her financial advisor told her that her overall portfolio rose in value by 1.1% last year. Erin noted in the newspaper that the equity fund lost 3.3% last year while the bond fund rose 7.7%. To the nearest 0.1%, what percentage of her portfolio was in the equity fund at the beginning of the year?

Solve for x: $\frac{x}{1.5^{2}}+3 x(1.5)^{2}=100$

Simplify: $\frac{4 r^{5} t^{6}}{\left(2 r^{2} t\right)^{3}}$

The price of the shares of Nadir Explorations Ltd. fell by 76% in the past year, to the current price of $0.45 per share. In dollars and cents, how much did the price of each share drop in the past year?

Solve: x - 0.025x = 341.25

Simplify: $\frac{\left(-r^{3}\right) 2 r^{4}}{\left(2 r^{-2}\right)^{2}}$

Simplify and collect like terms: 4(a² - 3a - 4) - 2(5a² - a - 6)

Solve the following pair of equations. Verify your solution. y = 2x 7x - y = 35

Simplify: a² x a³