Modeling Scenarios Algebraically

Modeling Scenarios Algebraically

For every scenario identify the constant, the coefficient, the dependent variable and the independent variable. Determine the linear equation that represents each scenario, solve the corresponding questions and verify your answer.

1. It costs a flat rate of $15 to go to the Calgary Stampede and $4 per ride.

1. You can buy work gloves from a site for $5 a pair plus $2 for shipping.

1. A banquet room rents for $50 plus $2 per person.

1. The cost of a pizza is $8.50 plus $1.35 per topping.

1. Winter Warehouse has winter jackets on sale at 25% off the regular price. If a jacket is on sale for $176.25, what is the regular price of the jacket?

1. Colin has a long-distance plan that charges 5 cents/min for long-distance calls. There is also a monthly charge of $4.95.

1. A rectangle has a length of 3.7 cm and a perimeter of 13.2 cm. Determine the width of the rectangle and the area of the rectangle.

1. Seven percent of a number is 56.7.

1. A parallelogram has one shorter side length of 1.2 cm and perimeter 6.6 cm. Write an equation that can be used to determine the length of the longer side. Solve the equation and verify the solution.

1. Stephanie has a job in sales. She earns a monthly salary of $2500, plus a commission of 8% of her sales. One month, Stephanie earns a total of $2780. How much did she sell that month?

1. The length of a Canadian football field, including the end zones, is 137.2 m. If a hose gallops at 13.4 /s, how much time would it take the horse to gallop the length of the field?

1. On Saturday morning, Marc had a quarter of his weekly allowance left. He spent a total of $6.50 on bus fares and a freshly squeezed orange juice on Saturday afternoon. He then had $2.25 left. How much is his weekly allowance?

1. Henri bought three jars of spaghetti sauce. He used a coupon that reduced the cost of each jar by $0.75. If he paid $6.72 altogether, what was the regular price of each jar?

1. Max and Sharifa are both saving to buy the same model of DVD player, which costs $99, including tax. Max already has $31 and decides to save $8.50 per week from now on Sharifa already has $25.50 and decides to save $10.50 per week from now on. Who can buy the DVD player first?

1. The average distance of Mercury from the sun is 57.9 million km. This distance is 3.8 million kilometers more than half the average distance of Venus from the sun. What is the average distance of Venus from the sun?

1. On a typical February day in Whitehorse the daily average temperature is -13.2⁰C. The low temperature is -18.1⁰C. What is the high temperature?

1. A square picture frame is made from wood that is 1.6 cm wide. The perimeter of the outside of the frame is 75.2 cm. What is the side length of the largest square picture that the frame will display?

1. For a fit and healthy person, the maximum safe heart rate during exercise is 220 minus their age, multiplied by four fifths. At what age is the maximum safe heart rate 164 beats/min?

1. An item increased in price by $4.95. This is a 9% increase. What did the item cost before the price increase?

1. A cell phone company offers two plans. Plan A: 120 free minutes, $0.75 per additional minute. Plan B: 30 free minutes, $0.25 per additional minute. Which time for calls will result in the same cost for both plans?

1. Two rental halls are considered for a wedding. Hall A costs $50 per person. Hall B costs $2000, plus $40 per person. Determine the number of people for which the halls will cost the same to rent.

1. Hendrik has a choice of 2 companies to rent a car. Company A charges $199 per week, plus $0.20 per kilometer driven. Company B charges $149 per week, plus $0.25 per kilometer driven. Determine the distance that Hendrik must drive for the two rental costs to be the same.

1. A cell phone company offers two different plans. Plan A: Monthly fee of $28, 30 free minutes, $0.45 per additional minute. Plan B: Monthly fee of $40, no free minutes plus $0.25 per minute. At what point will the monthly cost be the same for both plans.

1. An isosceles triangle has two equal sides of length 2.7 cm and perimeter 7.3 cm. Determine the length of the third side.