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Problem-Solving Equations for Unknowns

Learn to identify unknown variables, write equations, and solve math problems involving consecutive integers, rectangle dimensions, sail perimeter, and age differences.

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Problem-Solving Equations for Unknowns

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  1. Warm – Up September 3, 2008 • 5(-2w + 1) + 8w = 15 • -3x – 8 = -5x – 12 • |x + 8| + 3 = 14 • P = 2l + 2w, solve for w • -2x + 4 = 5 – 3x

  2. Solving Word Problems

  3. Tackling Word Problems • Identify every unknown with a “let” statement. • Typically your “x” will be the last word in the first sentence and the other unknown will be written in terms of x. • Write an equation for the given situation. • Solve the equation and be sure to find all unknowns.

  4. Find two consecutive integers whose sum is 45

  5. Find three consecutive integers whose sum is 48.

  6. Find three consecutive even integers whose sum is 72.

  7. Find three consecutive odd integers such that the sum of the smallest and 4 times the largest is 61.

  8. The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length.

  9. A triangular sail has a perimeter of 25 m. Side a is 2 m shorter than twice side b, and c is 3 m longer than side b. Find the length of each side.

  10. Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now?

  11. Melissa is 24 years younger than Joyce. In 2 years, Joyce will be 3 times as old as Melissa will be then. How old are they now?

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