Solving Averages, Investments, Piggy Bank Problems, and Geometry Using Different Methods, Exams of Algebra

Download Solving Averages, Investments, Piggy Bank Problems, and Geometry Using Different Methods and more Exams Algebra in PDF only on Docsity! 1310, 2.2 Applications and Word Problems We’ll study four kinds: Averages, Investments, Piggy Bank problems, and Geometry. Averages You know that the average of a collection of data is the sum divided by the number of data points. You may not know that you can do many different kinds of problems involving averages. 1. Suppose you want an A in a course that has 5 tests, all equally weighted, and you know 4 of your scores…you can then set a goal and see what you have to score on the last test. Suppose you have the following grades: 87, 88, 93, 89 and you need a 90% average to get an A…what do you need to score on the last test? 2. Suppose you know that 3 consecutive natural numbers average to 9. What are the numbers? What is the product of the numbers? What is the smallest number? 1 3. Let’s talk about a situation in which Janet is paid twice as much per hour as Mark is and Susan earns two dollars an hour less than Mark. If their average earnings per hour is $6.00 how much does Mark earn? 4. The sum of four consecutive even integers is 636. Find the average of the integers. 2 And there’s the ever popular piggy bank problems: 1. A piggy bank has 25 coins – all nickels and quarters – that add up to $5.65. How many nickels are there in the bank? Here, we’ve got two things to track: the number of coins and the value of the coins. We’ll work the problem in dollars. How many quarters? What is the product of the number of nickels and quarters? What is the average number of each type of coin? 5 2. Sam makes a deposit at the bank which is comprised of $5, $10, and $20 bills. If the number of $5 bills is three more than the number of $10 bills, the number of $20 bills is half the number of $5 bills, and the total deposit if $270, how many bills did he deposit? 6 And there’s geometry problems 1. A rectangle’s length is 7 inches greater than it’s width. If the perimeter of the rectangle is 110 inches, find its length and width. 2. A rectangular garden is three times as long as it is wide. If the total area of the garden is 432 square feet, find the length and width. 7 Another one: 016x 2  Factoring QF Algebraically Quickly: 081x 2  10 Now for today’s material: Solving for x using Complete the Square Given 012xx 2  Here’s the steps: 1. If a is a number other than one, divide both sides by a. Regard this as a new quadratic a = 1 b = _________ c = _________ 2. Take b and divide it by 2. Square the result and add it to both sides. 2 2 b       = Now we have: _____________________________________________________ 3. Rewrite the first 3 terms as 2) 2 b x(  4. Subtract c from both sides: 5. Take the square root of both sides: 11 6. Subtract 2 b from both sides 7. Report both values for x. The steps are: 1. If a is a number other that one, divide both sides by a. 2. Take b and divide it by 2. Square the result and add it to both sides. 3. Rewrite the first 3 terms as 2) 2 b x(  4. Subtract c from both sides: 5. Take the square root of both sides: 6. Subtract 2 b from both sides 7. Report both values for x. 12 Another one: 07x2x 2  1. If a is a number other that one, divide both sides by a. 2. Take b and divide it by 2. Square the result and add it to both sides. 3. Rewrite the first 3 terms as 2) 2 b x(  4. Subtract c from both sides: 15 5. Take the square root of both sides: 6. Subtract 2 b from both sides 7. Report both values for x. The steps: 16 1. If a is a number other that one, divide both sides by a. 2. Take b and divide it by 2. Square the result and add it to both sides. 3. Rewrite the first 3 terms as 2) 2 b x(  4. Subtract c from both sides: 5. Take the square root of both sides: 6. Subtract 2 b from both sides 7. Report both values for x. More practice 05x3x 2  17 The steps: 1. If a is a number other that one, divide both sides by a. 2. Take b and divide it by 2. Square the result and add it to both sides. 3. Rewrite the first 3 terms as 2) 2 b x(  4. Subtract c from both sides: 5. Take the square root of both sides: 6. Subtract 2 b from both sides 7. Report both values for x. 22x 6x 3.5   20 The steps: 1. If a is a number other that one, divide both sides by a. 2. Take b and divide it by 2. Square the result and add it to both sides. 3. Rewrite the first 3 terms as 2) 2 b x(  4. Subtract c from both sides: 5. Take the square root of both sides: 6. Subtract 2 b from both sides 7. Report both values for x. 22x 4x 5 0   21 Solve 2x 2x 3 0   Factoring: CTS: 22