Read the story problem: "The sum of two consecutive odd numbers equals twenty-four. What are both of the numbers?"
Translate the facts from the word problem into mathematical values. Let x represent the first of the numbers and use x + 2 to represent the second of the consecutive numbers, remember to use + 2 because the problem calls for two consecutive odd numbers.
Write an algebraic equation to include the rest of the values from the word problem: x + (x + 2) = 24.
Combine like terms: 2x + 2 = 24. Subtract 2 from both sides of the equation: 2x = 22. Divide both sides of the equation by 2: x = 11. Therefore, the first number is 11 and after adding two, the second number is 13. Check the math for validity: 11 + 13 = 24, which is a true statement.
Write an algebraic equation from the following story problem: "A 21-foot board is cut into two pieces in such a way that the first piece is 3 feet shorter than the second. What are the lengths of each piece?"
Convert the facts into mathematical value. Let x represent the second board and x - 3 represent the first board. Set the facts equal to 21 because the board is 21 feet long: x + (x - 3) = 21. After following the correct operations, you should find that the first board is nine feet long and the second is 12.
Write an algebraic equation from the following story problem: "Two squared plus a number has the same value as two plus six. What is the number?"
Translate the literal values to mathematical ones using x to represent the unknown number: 2^2 + x = 2 + 6. The equation simplifies to 4 + x = 8 and after following the basic operations, you should find that the solution is x = 4.