1. Equations & Inequalities

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?D = RT for R

A job pays an annual salary of $57,900, which includes a holiday bonus of $1500. If paychecks are issued twice a month, what is the gross amount for each paycheck?

For an international telephone call, a telephone company charges $0.43 for the first minute, $0.32 for each additional minute, and a $2.10 service charge. If the cost of a call is $5.73, how long did the person talk?

A repair bill on a sailboat came to $2356, including $826 for parts and the remainder for labor. If the cost of labor is $90 per hour, how many hours of labor did it take to repair the sailboat?

An automobile repair shop charged a customer $1182, listing $357 for parts and the remainder for labor. If the cost of labor is $75 per hour, how many hours of labor did it take to repair the car?

The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

Exercises 19–20 involve markup, the amount added to the dealer's cost of an item to arrive at the selling price of that item.The selling price of a refrigerator is $1198. If the markup is 25% of the dealer's cost, what is the dealer's cost of the refrigerator?

Including a 17.4% hotel tax, your room in Chicago cost $287.63 per night. Find the nightly cost before the tax was added.

Including a 10.5% hotel tax, your room in San Diego cost $216.58 per night. Find the nightly cost before the tax was added.

After a 20% reduction, you purchase a television for $336. What was the television's price before the reduction?

An electronic pass for a toll road costs $30. The toll is normally $5.00 but is reduced by 30% for people who have purchased the electronic pass. Determine the number of times the road must be used so that the total cost without the pass is the same as the total cost with the pass.

You are choosing between two gyms. One gym offers membership for a fee of $40 plus a monthly fee of $25. The other offers membership for a fee of $15 plus a monthly fee of $30. After how many months will the total cost at each gym be the same? What will be the total cost for each gym?