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Math Problem-solving Practice: Equations & Puzzles

Solve unique math problems involving digits, ages, and fractions using systems of equations. Examples and practice questions provided for comprehensive learning.

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Math Problem-solving Practice: Equations & Puzzles

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  1. Warm up • An airplane flies 3000 mi in 4 h, but takes 5 h to make the return trip. What is the plane’s speed in still air? What is the speed of the wind?

  2. Lesson 9-7 Puzzle Problems Objective: To use systems of equation to solve digit, age & fraction problems

  3. Example • The sum of the digits of a two digit number is 15. If the digits are reversed, the new number obtained is 9 more than the original. Find the original number.

  4. Example • Seven years ago, my father's age was five times mine. Right now,his age is the sum of our two ages 7 years ago. How old am I?

  5. Example • The denominator of a fraction is 2 more than the numerator. If 3 is added to both the numerator and denominator, the new fraction is equal to 5/6. Find the original fraction.

  6. Practice • Gabrielle is twice Nicole’s age. In six years, the sum of their ages will be 30. How old are they now?

  7. Practice • If 5 is subtracted from the numerator of a fraction, the value of the resulting fraction is ¼ .If 6 is added to the denominator of the original fraction, the value of the new fraction is ½. What is the original fraction?

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