Algebraic Equations (Speedy Study Guides). Speedy Publishing

      ALGEBRAIC EQUATIONS

      Writing Algebraic Equations

      Problem: Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?

      Solution: Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem:

      17 + x = 68

      We can subtract 17 from both sides of the equation to find the value of x.

      68 - 17 = x

      Answer: x = 51, so Jeanne needs $51 to buy the game.

      In the problem above, x is a variable. The symbols 17 + x = 68 form an algebraic equation. Let’s look at some examples of writing algebraic equations.

      Example 1: Write each sentence as an algebraic equation

      Sentence

      A number increased by nine is fifteen.

      Twice a number is eighteen.

      Four less than a number is twenty.

      A number divided by six is eight.

      Algebraic Equation

      y + 9 = 15

      2n = 18

      x - 4 = 20

      k

      6

      = 8

      Example 2: Write each sentence as an algebraic equation.

      Sentence

      Twice a number, decreased by twenty-nine, is seven.

      Thirty-two is twice a number increased by eight.

      The quotient of fifty and five more than a number is ten.

      Twelve is sixteen less than four times a number.

      Algebraic Equation

      2t - 29 = 7

      32 = 2a + 8

      50

      n + 5

      = 10

      12 = 4x - 16

      Example 3: Write each sentence as an algebraic equation

      Sentence

      Eleni is x years old. In thirteen years she will be twenty-four years old.

      Each piece of candy costs 25 cents. The price of h pieces of candy is $2.00.

      Suzanne made a withdrawal of d dollars from her savings account. Her old balance was $350,

      and her new balance is $280.

      A large pizza pie with 15 slices is shared among p students so that each student’s

      share is 3 slices.

      Algebraic Equation

      x + 13 = 24

      25h = 200

      350 - d = 280

      15

      p

      = 3