2-3: Applications of Equations Learning Goals: Solve real-life application problems © 2007 Roy L. Gover (www.mrgover.com)

Important Idea Mathematics in the world outside school is used to solve problems which are often described verbally. The verbal problems must be translated into equivalent mathematical statements.

Important Idea Steps for solving application problems: Read Read again- write down what you are given and what you want to know. Draw pictures and label if appropriate.

Important Idea Steps for solving application problems: Write an equation(s) showing relationships between what you are given and what you want to know. Solve. Check your answers for reasonableness.

Example The average of two real numbers is 41.125, and their product is 1683. Use your graphing calculator to find the two numbers. 44 & 38.25

Try This The average of two real numbers is 39.625, and one number is 1500 times the reciprocal of the other. Use your graphing calculator to find the two numbers. 48 & 31.25 48 & 31.25

Example A rectangle is twice as wide as it is high. If it has a area of 24.5 square inches, what are its dimensions? Solve algebraically. 7X3.5 in.

Try This The width of a rectangle is three times it height. If it has an area of 60.75 square feet, what are its dimensions? Solve algebraically. 7X3.5 in. 13.5 ft. by 4.5 ft.

Example A rectangular box with a square base and no top is to have a volume of 30,000 cm3. If the surface area of the box is 6000cm2, what are the dimensions of the box? Use your graphing calculator. 21.7 X 21.7 X 63.71 cm or 64.29 X 64.29 X 7.26 cm

Try This A storage locker in the shape of a box with a square floor has a volume of 70,000 in3. If the surface area of the four walls and the top of the locker is 10,000 in2, what are the dimensions of the locker. Use your calculator. 21.7 X 21.7 X 63.71 cm or 64.29 X 64.29 X 7.26 cm

Solution s h 30.97 by 30.97 by 72.98 or 80.85 by 80.85 by 10.71

r is the annual interest rate Definition Simple Interest: where p is the principal r is the annual interest rate t is time in years

Example A stock pays dividends at a rate of 12% per year and a savings account pays 6% interest per year. How much of a $9000 investment should be put in stock and how much in savings to obtain a return of 8% per year on the total investment.

Definition where d is distance r is rate (speed) t is time

Example A pilot wants to make a 840 mile round trip from Dallas to Houston and back in 5 hours. There will be a headwind of 30 mph going to Houston and a 40 mph tailwind returning to Dallas. At what constant speed should the plane be flown.

Try This A canoeist paddled a total of 11 hours on a 48 km round trip to Bear Lake. The upstream trip was against a current of 3 km/hr. The return trip was with a current of 2 km/hr. At what speed could he paddle the canoe in still water. 6 km/hr

Example A landscaper wants to put a cement walk of uniform width around a rectangular garden that measures 24 by 40 ft. She has enough cement to cover 660 sq. ft. How wide should the walk be in order to use all the cement?

Example A box with no top that has a volume of 1000 cu. in. is to be constructed from a 22 by 30 in. sheet of cardboard by cutting squares of equal size from each corner and folding up the flaps. What size square should be cut from each corner?

Example A car radiator contains 12 quarts of fluid, 20% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the resulting mixture is 50% antifreeze?

Try This A chemist has 30 ml of a 40% acid solution in a test tube. How much of the solution should be poured off and replaced with pure acid so that the new mixture is 70% acid? 15 ml

Lesson Close Without looking at your notes, what are the steps for solving an application problem?

Practice Pg 105 3,5,7,9,11,13,15, 17,19,21,23