How do you Write an Algebraic Equation for a Word Problem?

To write an algebraic equation for a word problem, identify the unknowns, assign variables, and translate the problem's statements into mathematical expressions using operations like addition, subtraction, multiplication, and division. Ensure the equation accurately represents the relationships described in the problem.

Let's discuss this in detail.

What is an Algebraic Equation?

An algebraic equation is a mathematical statement that shows the equality of two expressions by connecting them with an equal sign (=).

The expressions on either side of the equal sign involve variables (letters representing unknown values), constants (fixed numbers), and mathematical operations like addition, subtraction, multiplication, and division.

Steps to Write an Algebraic Equation for a Word Problem

• Step 1: Read the Problem Carefully

Understand what the problem is asking.

• Step 2: Identify Keywords

Look for keywords that indicate mathematical operations:

• Addition: sum, more than, increased by, total, plus
• Subtraction: difference, less than, decreased by, minus
• Multiplication: product, times, multiplied by, of
• Division: quotient, divided by, per, out of
• Equality: is, are, will be, gives, equals

• Step 3: Assign Variables

Assign a variable (like x or y) to represent the unknown quantity you are trying to find.

• Step 4: Translate the Words into an Equation

Convert the phrases into mathematical expressions using the variable you’ve assigned.

Example: If the problem states "A number increased by 5 is 12," let the unknown number be x. The equation would be: x + 5 = 12

• Step 5: Write the Equation

Put together all parts of the problem into a single equation.

• Step 6: Solve the Equation

Solve the equation for the variable to find the answer.

Example for Algebraic Equation for a Word Problem

Problem: "Three times a number decreased by 4 is 11. What is the number?"

Solution:

• Identify the unknown: Let the unknown number be x.
• Translate the words into math:
  • "Three times a number" translates to 3x.
  • "Decreased by 4" translates to 3x − 4.
  • "Is 11" translates to = 11.
• Write the equation: 3x − 4 = 11
• Solve the equation:
  • Add 4 to both sides: 3x = 15.
  • Divide by 3: x = 5.

Answer: The number is 5.

Practice Questions

Q1: A number decreased by 4 is 10. Find the number.

Q2: The product of a number and 5 is 35. Find the number.

Q3: If the length of a rectangle is twice its width and its perimeter is 36 units find the dimensions of the rectangle.

Q4: A father is three times as old as his son. If the sum of their ages is 48 years find their ages.

Q5: Two numbers differ by the 8 and their sum is 48. Find the numbers.

Q6: The sum of a number and twice another number is 22. If the second number is 3 less than the first number find the numbers.

Q7: A shop sells pencils at $2 each and erasers at $3 each. If a student buys a total of 10 items and spends $24 how many pencils and erasers did the student buy?

Q8: The difference between a number and 7 is equal to twice the number decreased by 5. Find the number.

Q9: The sum of three consecutive integers is 51. Find the integers.

Q10: A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer paid $50 for a rental how many miles did they drive?

Conclusion

Writing algebraic equations for the word problems requires translating the given conditions into the mathematical expressions. By identifying key variables and relationships described in the problem we can set up equations that model the situation. Practice with the various problems helps in understanding how to form and solve these equations effectively. The Mastery of this skill is crucial for the solving the real-world problems in algebra and beyond enhancing both the problem-solving and analytical abilities.