6.3 Applications of Algebra 313 Phrase Mathematical expression Six more than a number x 6 + A number increased by 3 x 3 + Four less than a number x 4 − A number decreased by 9 x 9 − Twice a number 2x The product of 7 and a number 7x The quotient of a number and 8 x 8 Four times a number 4x 3 decreased by a number x 3 − The difference between a number and 5 x 5 − Sometimes the phrase that must be converted to a mathematical expression involves more than one operation. Phrase Mathematical expression Four less than 3 times a number x3 4 − Ten more than twice a number x2 10 + The sum of 5 times a number, and 3 x5 3 + Eight times a number, decreased by 7 x8 7 − The word is often represents the equal sign. Matching Verbal Statements to Equations Phrase Mathematical equation Six more than a number is 10. x 6 10 + = Five less than a number is 20. x 5 20 − = Twice a number, decreased by 6 is 12. x2 6 12 − = A number decreased by 13 is 6 times the number. x x 13 6 − = The following is a general procedure for solving word problems. PROCEDURE SOLVING WORD PROBLEMS 1. Read the problem carefully at least twice to be sure that you understand it. 2. If possible, draw a sketch to help visualize the problem. 3. Identify which quantity you are being asked to determine. Choose a letter to represent this unknown quantity. Write down exactly what this letter represents. 4. Write the word problem as an equation. 5. Solve the equation for the unknown quantity. 6. Answer the question or questions asked. 7. Check the solution.
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