3Choose something to represent the first integer---let’s choose “x”. x = first integerThen to represent a consecutive integer, that would mean the integer right after x or x+1.x +1 = second integerThe sum of two consecutive integers is Find the integers.Means add togetherThe hard part is done!x + x +1 = 137Now solve for x to get the first integer. Just add 1 to get the second.
4The sum of two consecutive integers is 65. What is the second number? Let x = the 1st numberLet x + 1 = the 2nd numberSum means???x = 32x + 1 = 33x + x + 1 = 65= 65 2x + 1 = 65-1 -12x = 64
5The sum of two consecutive integers is 27. What are the two integers?
7The sum of two consecutive integers is 9. What are the two integers?
8Let’s consider a problem that asked for consecutive even integers Let’s consider a problem that asked for consecutive even integers. Your first integer will still be “x”.x = first integerThen to represent a consecutive even integer, you would need to add 2 instead of 1 and get x+2.x +2 = second integerThe sum of two consecutive even integers is Find the integers.Now you are ready to solve.x + x +2 = 626
9Let’s consider a problem that asked for consecutive odd integers Let’s consider a problem that asked for consecutive odd integers. Your first integer will still be “x”.x = first integerNow what would you do to x to get to the next odd integer?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?x +2 = second integerSo 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.
10The perimeter of a rectangle with sides of lengthx and 2x - 1The perimeter of a rectangle is the sum of the lengths of the sidesxIn words: sides sides2 sides2 sides2x - 1Translate: 2(x) (2x-1)Then: x x-26x simplify
11General Strategy for Problem Solving 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.
12TRANSLATE the problem into an equation. SOLVE the equation.INTERPRET the results: Check the proposed solution in the stated problem and state your conclusion.
13FINDING 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?
14UNDERSTAND. Read and reread the problem UNDERSTAND. Read and reread the problem. Recall that a percent decrease means a percent of the original price. Let’s guess that the original price of the computer is $ 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 = $ Our guess is incorrect, but we now have an idea of how to model this problem
152. TRANSLATE: In words: Original price of computer minus 8% of original priceisnew priceTranslate:x-0.08 x=2160
160.92x = 2162 Divide both sides of equation 3. SOLVE the equationx – 0.08x = 21620.92x = Divide both sides of equationx = Solution
174. INTERPRET.Check: If the original price of the computer was $2350, the new price is$2350 – (0.08)($2350) = $ $188= $2162State: The original price of the computer was $2350