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Solution: Let The key is to focus on the phrase “3 times the sum.” This prompts us to group the sum within parentheses and then multiply by 3.
Step 2: Identify the variables by assigning a letter or expression to the unknown quantities. Eight times a number is decreased by three times the same number, giving a difference of 20. Algebra simplifies the process of solving real-world problems. This is done by using letters to represent unknowns, restating problems in the form of equations, and offering systematic techniques for solving those equations. If the smaller of two consecutive integers is subtracted from two times the larger, then the result is 17. If the perimeter is 102 inches, then find the measure of each side. If the perimeter is 21 inches, find the measure of each side. A triangle has sides whose measures are consecutive integers. These problems can sometimes be solved using some creative arithmetic, guessing, and checking. Example 4: The difference between two integers is 2. It is worth mentioning again that you can often find solutions to simple problems by guessing and checking. Solving in this manner is not a good practice and should be avoided. The larger integer is 6 less than twice the smaller. Solution: Use the relationship between the two integers in the second sentence, “The larger integer is 6 less than twice the smaller,” to identify the unknowns in terms of one variable. This is so because the numbers are chosen to simplify the process of solving, so that the algebraic steps are not too tedious. Jill has 3 fewer half-dollars than she has quarters. The average speeds for the planes are 450 miles per hour and 395 miles per hour. Bill leaves 1 hour earlier than Ted and travels at an average rate of 60 miles per hour. She has 1 fewer than three times as many tens as she does five-dollar bills. He has 3 more dimes than quarters and 5 more nickels than quarters. She has twice as many quarters than she does half-dollar coins and the same amount of half-dollar coins as one-dollar bills. He has 2 more than 3 times as many ones as he does five-dollar bills and 1 fewer ten- than five-dollar bills. If one car averages 55 miles per hour and the other averages 65 miles per hour, then how long will it take for them to separate a distance of 300 miles? Two planes leave the airport at the same time traveling in opposite directions.Begin by working through the basic steps outlined in the general guidelines for solving word problems. You learn how to set up algebraic equations with easier problems, so that you can use these ideas to solve more difficult problems later. Twice some number is subtracted from 30 and the result is 50. Example 3: A larger integer is 2 less than 3 times a smaller integer. Example 5: The sum of two consecutive even integers is 46. Solution: The key phrase to focus on is “consecutive even integers.” 3 when identifying the variables for consecutive odd integers.