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Introduction to Problem Solving quiz

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  • What are the five steps to solving a word problem?
    The five steps are: understand the problem, build an equation, solve the equation, state the answer, and check the solution.
  • How do you define variables when solving a word problem about a rectangle's perimeter?
    Assign letters to each quantity, such as l for length, w for width, and p for perimeter, to make equations easier to build and solve.
  • What is the formula for the perimeter of a rectangle in terms of length and width?
    The formula is P = 2l + 2w, where P is perimeter, l is length, and w is width.
  • How do you translate 'length is four times its width' into an algebraic equation?
    You write l = 4w, where l is length and w is width.
  • What should you do if a word problem involves shapes or geometry?
    Draw a picture to help model the situation and clarify relationships between variables.
  • How do you solve for width if the perimeter is 500 yards and length is four times width?
    Substitute l = 4w into P = 2l + 2w, set P = 500, and solve for w to get w = 50.
  • After finding the width, how do you find the length in the rectangle problem?
    Use the relationship l = 4w and substitute the value of w to find l.
  • Why is it important to check your solution in the context of the problem?
    Checking ensures the values are reasonable and fit the real-world scenario described in the problem.
  • What are consecutive integers?
    Consecutive integers are whole numbers that follow each other in order, differing by one.
  • How do you represent two consecutive integers algebraically?
    Let the first integer be x, then the next consecutive integer is x + 1.
  • How do you solve a problem where two consecutive page numbers sum to 23?
    Set up the equation x + (x + 1) = 23, solve for x, and find both page numbers.
  • What are consecutive even integers and how do they differ from consecutive integers?
    Consecutive even integers are even numbers that follow each other, differing by two instead of one.
  • How do you represent two consecutive even integers algebraically?
    Let the first even integer be x, then the next is x + 2.
  • How do you solve for two consecutive even integers that sum to 286?
    Set up the equation x + (x + 2) = 286, solve for x, and find both integers.
  • Why is it important to check if you are dealing with consecutive even, odd, or regular integers in word problems?
    Because the difference between the numbers changes (1 for regular, 2 for even/odd), affecting how you set up the equations.