An algebraic equation is a mathematical statement that shows the equality of two expressions by connecting them with an equal sign (=).
- 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.
Steps to Write an Algebraic Equation
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. For example, "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.
Solved Example
Problem 1: "Three times a number decreased by 4 is 11. What is the number?"
1. Identify the unknown: Let the unknown number be x.
2. Translate the words into math:
"Three times a number" translates to 3x.
"Decreased by 4" translates to 3x − 4.
"Is 11" translates to = 11.
3. Write the equation: 3x − 4 = 11
4. Solve the equation:
Add 4 to both sides: 3x = 15.
Divide by 3: x = 5.
The number is 5.
Problem 2: Four times a number is equal to 36. Find the number.
Step 1: Let the unknown number be x.
Step 2: Translate the statement.
- "Four times a number" → 4x
- "is equal to 36" → = 36
Step 3: Write the equation: 4x = 36
Step 4: Solve. x = 36/4 = 9
The number is 9.
Problem 3: A father is 4 times as old as his son. The sum of their ages is 50 years. Find their ages.
Step 1: Let the son's age be x.
Step 2: Father's age = 4x.
Step 3: Form the equation using the total age:
x+4x = 50
5x = 50
x = 10
Father's age: 4×10 = 40
Son = 10 years, Father = 40 years.
Problem 4: The sum of three consecutive integers is 72. Find the integers.
Step 1: Let the first integer be x.
The next two integers are: x+1 ,x+2
Step 2: Form the equation. x + (x+1) + (x+2) = 72
Step 3: Simplify:
3x+3 = 72
3x = 69
x = 23
Step 4: Find the integers: 23, 24, 25
The integers are 23, 24, and 25.
Problem 5: The length of a rectangle is 3 times its width. If the perimeter is 64 units, find its dimensions.
Step 1: Let the width be x.
Length: 3x
Step 2: Use the perimeter formula: 2(l+w) = 64
Substitute values:
2(3x+x) = 64
2(4x) = 64
8x = 64
x = 8
Step 3: Find the length.
3×8 = 24
Width = 8 units, Length = 24 units.
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.
