AlgebraStructure & Method · Book 1All Chapters

Applications

9-7Puzzle Problems

Overview

Digit puzzles and similar problems become systems of equations after careful translation.

Key ideas

  • Define each digit/quantity as a variable.
  • Use given clues to write each equation.
  • Solve the system; check restrictions.

Worked examples

Example 1

Problem. Sum of digits of a 2-digit number is 9; reversed number is 27 less. Find it.

Solution. t + u = 9, (10u + t) = (10t + u) − 27 → 9u − 9t = −27 → u − t = −3. With t + u = 9: t = 6, u = 3. Number = 63.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Digits sum to 7; reverse is 9 more. Find number.

  2. 2.

    Two numbers: sum 14, product 48. Find them.

  3. 3.

    Sum 20, difference 6.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    I am thinking of two numbers. Their sum is 15. If I double the first and add the second, I get 22. Find the numbers.

  2. 2.

    A collection of 20 coins (dimes and quarters) is worth $3.50. How many of each coin?