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. Helpful Hint Order matters when subtracting and also dividing, so be especially careful with these translations. Addition (+ Subtraction (-) Multiplication ( . ) Division (=) Equality (= Sum Difference of Product Quotient Equals Plus Minus Times Divide Give Added to Subtracted from Multiply Into Is/was/should be More than Less than Twice Ratio Yields Increased by Decreased by Of Divided by Amounts to Total Less Represents Is the same as The sum of six and twice a number is equal to seven less than the number. Find the number. A 23-inch piece of string is to be cut into two pieces so that the length of the longer piece is three more than four times the shorter piece. If x represents the length of the shorter piece, find the lengths of both pieces. Find three consecutive integers whose sum is -114.The room numbers of two adjacent classrooms are two consecutive even numbers. If their sum is 654, find the classroom numbers. The perimeter of a rectangular billboard is 60 feet and the billboard has a length 6 feet longer than its width. Find the dimensions of the billboard ? feet jax feet Hertz Car Rental charges a daily rate of $39 plus $0.20 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $95. How many miles did you drive? The left and right page numbers of an open book are two consecutive integers whose sum is 469. Find these page numbers