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OBJECTIVES 1. Write algebraic expressions that can be simplified 2. Apply the steps for problem solving

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Consecutive Integer Problems © 2002 by Shawna Haider

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The sum of two consecutive integers is 137. Find the integers. x = first integer Choose something to represent the first integer---lets choose x. Then to represent a consecutive integer, that would mean the integer right after x or x+1. x +1 = second integer Means add together Now solve for x to get the first integer. Just add 1 to get the second. x + x +1 = 137

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The sum of two consecutive integers is 65. What is the second number? Let x = the 1 st number Let x + 1 = the 2 nd number Sum means??? x + x + 1 = 65 2x + 1 = 65 2x = x = 32 x + 1 = = 65

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The sum of two consecutive integers is 27. What are the two integers?

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What two consecutive integers have a sum of 39?

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The sum of two consecutive integers is 9. What are the two integers?

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Lets consider a problem that asked for consecutive even integers. Your first integer will still be x. x = first integer Then to represent a consecutive even integer, you would need to add 2 instead of 1 and get x+2. x +2 = second integer The sum of two consecutive even integers is 626. Find the integers. x + x +2 = 626 Now you are ready to solve.

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Most students initial reaction is add 1 but try x = 3 (an odd integer) and see what happens when you add 1. Not an odd integer. So what would you add to 3 to get the next odd integer? Lets consider a problem that asked for consecutive odd integers. Your first integer will still be x. x = first integer Now what would you do to x to get to the next odd integer? x +2 = second integer So whether the problem says even integer or odd integer, the setup would look the same. If x happens to be odd then when you add 2 you will be at the next odd integer and if it happens to be even and you add 2 you will be at the next even integer.

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The perimeter of a rectangle with sides of length x and 2x - 1 2x - 1 x The perimeter of a rectangle is the sum of the lengths of the sides In words: 2 sides + 2 sides 2 sides Translate: 2(x) + 2(2x-1) Then: 2x + 4x-2 6x - 2 simplify

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General Strategy for Problem Solving 1.UNDERSTAND the problem. During this step, become comfortable with the problem. Some ways of doing this are: Read and reread the problem. Choose a variable to represent the unknown. Construct a drawing. Propose a solution and check. Pay careful attention to how you check your proposed solution. This will help when writing an equation to model the problem.

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2.TRANSLATE the problem into an equation. 3.SOLVE the equation. 4.INTERPRET the results: Check the proposed solution in the stated problem and state your conclusion.

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FINDING THE ORIGINAL PRICE OF A COMPUTER Suppose that a computer store just announced an 8% decrease in the price of a particular computer model. If this computer sells for $2162 after the decrease, find the original price of this computer. What are the steps to solving this problem?

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1.UNDERSTAND. Read and reread the problem. Recall that a percent decrease means a percent of the original price. Lets guess that the original price of the computer is $2500. The amount of decrease is then 8% of $2500, or (0.08)($2500) = $200. This means that the new price of the computer is the original price minus the decrease, or $ $200 = $2300. Our guess is incorrect, but we now have an idea of how to model this problem

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2. TRANSLATE: In words: Original price of computer Original price of computer minus 8% of original price is new price Translate:x-0.08 x=2160

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3. SOLVE the equation x – 0.08x = x = 2162 Divide both sides of equation x = 2350 Solution

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4. INTERPRET. Check: If the original price of the computer was $2350, the new price is $2350 – (0.08)($2350) = $ $188 = $2162 State: The original price of the computer was $2350

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