MA42: TRIGONOMETRY UNIT 9.6 – SOLVE REAL WORLD PROBLEMS DO NOT WRITE ON

USING GRAPHS / INVERSE MATRICES THIS SHEET!

DO YOUR WORK ON A SEPARATE SHEET!

LIVE GREEN…Return this sheet unwritten on and undamaged!

1) Finding the Equilibrium Point – The demand and supply functions for a new calculator are:

Demand Equation

Supply Equation

where is the price in dollars and represents the number of units. Find the equilibrium point for this market. The equilibrium point is the price and number of units that satisfy both the demand and supply equations.

2) Dawn woke up just as the sun was coming up. She went to Staples and bought pens and

pencils for school. Pens cost $1.25 each and pencils cost 0.25 each. She bought a total of 36 writing utensils. Her total bill (do not include tax) was $14. How many pencils did she buy?

3) Your family is planning a 7 day trip to Florida. You estimate that it will cost $275 per day in

Tampa and $400 per day in Orlando. Your total budget for the 7 days is $2300. How many days should you spend in each location?

4) A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The

investor wants an annual interest income of $990 from the investment. What amount should be invested in the 7.5% bond?

5) At a local high school city championship basketball game, 1435 tickets were sold. A student

admission ticket cost $1.50 and an adult admission ticket cost $5.00. The total ticket receipts for the basketball game were $3552.50. How many of each type of ticket were sold?

6) With a tailwind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the

Piper can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the Piper.

7) A rotating sprinkler head with a range of 50 feet is to be placed in

the center of a rectangular field (see picture to right). If the area of the field is 4000 ft² and the water is to just reach the corners, find the dimensions of the field.

8) Find equations of the two lines that are tangent to the circle and pass through the

point (Hint: Let and determine conditions on that will ensure that the system has only one solution.)

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