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
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 = 64 2 2 x = 32 x + 1 = 33 32 + 33 = 65
The sum of two consecutive integers is 27. What are the two integers?
What two consecutive integers have a sum of 39?
The sum of two consecutive integers is 9. What are the two integers?
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.
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.
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
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.
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.
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?
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 $2500 - $200 = $2300. Our guess is incorrect, but we now have an idea of how to model this problem
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
3. SOLVE the equation x – 0.08x = 2162 0.92x = 2162 Divide both sides of equation 0.92 0.92 x = 2350 Solution
4. INTERPRET. Check: If the original price of the computer was $2350, the new price is $2350 – (0.08)($2350) = $2350 - $188 = $2162 State: The original price of the computer was $2350