Exam 2: Review and Applications of Algebra

An item listed at 40% above cost was sold by a dealer during a special sale at a 15% reduction from the list price. What did the item cost the dealer if it was sold for $23,765.00?

A city's commercial construction by-laws require five parking spaces for every 100 square metres of retail rental space in a shopping centre. Four percent of the parking spaces must be large spaces for the physically handicapped. Of the remainder, there must be 40% more regular-size spaces than "small-car" spaces. How many parking spaces of each type are required for a 27,500 square metre shopping centre?

Evaluate to six-figure accuracy: $\frac{1-(1.00 \overline{6})^{-32}}{0.00 \overline{6}}$

If the euro is worth 32% more than the Canadian dollar, how much less (in percentage terms) is the Canadian dollar worth than the euro?

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

During the last 30 years the price of gasoline has increased by 440%. If the current price per litre is $0.589, what was it 30 years ago?

Use the graphical method to solve the following pair of equations. x - 3y = 3 y = -2

The net amount after a 34% reduction on $180 is $122.50.

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?

Solve for x to five-figure accuracy: $\frac{x}{1.08^{3}}+\frac{x}{2}(1.08)^{4}=\$ 850$

Solve for the unknown variable: 3(x - 6) + 5x - 2(2x - 3) = 0

What is $47.50 increased by 320%?

Solve the following pair of equations. Verify your solution. 37x - 63y = 235 18x + 26y = 468

Solve for x and y: x + y = 40 -x + y = -20

What amount reduced by 80% leaves $100?

A caterer has the following price structure for banquets. The first 20 meals are charged the basic price per meal. The next 20 meals are discounted by $2 each and all additional meals are each reduced by $3. If the total cost for 73 meals comes to $1686, what is the basic price per meal?

Evaluate the following: $\frac{\left(r^{9}\right)^{2}\left(r^{6}\right)}{r^{12}}$ =

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?

Solve the following pair of equations. Verify your solution. y - 3x = 11 5x + 30 = 4y

If operating expenses are 40% of revenue, by what percentage does revenue exceed operating expenses?