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Word Problems Involving Linear and Quadratic Equations

             Translate the following phrases into mathematical expressions or equations. The sum of a number and six is eleven. â‡'x+6 = 11 .
             2. The sum of a number and twice that number is eighteen. â‡'x+2x = 18 .
             3. The sum of three consecutive integers is twenty-one. â‡'x+(x+1)+(x+2) = 21 .
             4. The sum of two consecutive even integers is thirty-four. â‡'x+(x+2) = 34 .
             5. The sum of the squares of two consecutive integers is thirteen. â‡'x2 +(x+1)2 = 13 .
             6. Three more than twice a number is fifteen. â‡'2x+3 = 15 .
             7. Four times a number increased by two is ten. â‡'4x+2 = 10 .
             8. Nine less than thrice a number is eighteen. â‡'3xâˆ'9 = 18 .
             9. Nine less thrice a number is eighteen. â‡'9âˆ'3x = 18 .
             10. Five times a number decreased by twelve is fifty-eight. â‡'5xâˆ'12 = 58 .
             11. The sum of a number and half of that number is nine. â‡'x+ 1 2x = 9 II. .
             Steps in Solving a Word Problem.
             1. Read the problem carefully and make sure the situation is thoroughly understood. .
             2. Identify the quantities, both known and unknown, that are involved in the problem. .
             3. Select one of the unknown quantities and represent it by a variable and then express any other unknowns in terms of this variable, if possible. .
             4. Search the problem for information that tells what quantities or combinations of them are equal. .
             5. Often, making a sketch helps to carry out step 4. .
             6. Write an equation using the algebraic expressions found in step 5. Carrying through the calculations with an initial guess sometimes help to clarify the relationship between variables. .
             7. Solve the equation obtained in step 6. .
             8. Check the solution in the original problem. This step is critical since we want a solution of the stated problem rather than of the equation that we write. .
             III. Word Problems Involving Linear Equations.
             1. Number Problems.
             A. The sum of two numbers is 23 and their difference is 5. Find the numbers. .
             B. One-fifth of a certain number is two more than one-sixth of the number.


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