Applications of Algebra

Chapter Sections 3.1 – Changing Application Problems into Equations 3.2 – Solving Application Problems 3.3 – Geometric Problems 3.4 – Motion, Money and Mixture Problems Chapter 1 Outline

Changing Application Problems into Equations

Word or Phrase Statement Algebra Operations Statement Algebra Added to More than Increased by The sum of Addition A number added to 3 2 more than a number A number increased by 7 The sum of a 1 and a number 3 + x x + 2 x + 7 1 + x Subtracted from Less than Decreased by Difference between The difference in The difference of Subtraction A number subtracted from 3 5 less than a number A number decreased by 8 The difference between 4 and a number The difference in a number and 6 The difference of x squared and y squared 3 - x x – 5 x – 8 4 - x x – 6 x2- y2 Multiplied by The product of Twice a number Three times a number Of (when used with a percent or fraction) Multiplication 8 multiplied by a number The product of 9 and a number 25% of a number 8x 9x 2x 3x 0.25x Divided by The quotient of The ratio of Division 13 divided by a number The quotient of a number and 11 The ratio of a number and 17

Expressions with Percents Percent means “per one hundred.” Statement Expression A 7.5% sales tax on c dollars The cost, c, increased by 7.5% The cost, c, reduced by 25% 0.075c c + 0.075c c – 0.25c

Translating into Equations The word is often means is equal to and is represented by an equal sign. Statement Equation Six times a number is 42. Five more than twice a number is 4. 7 decreased by a number is 4 more than twice the number. The sum of a number and the number increased by 4 is 60. 6x = 42 2x + 5 = 4 7- x = 2x + 4 x + (x + 4) = 60