Applied Problem Solving
How to Solve Ratio Word Problems
A structured, repeatable framework to translate word problems into mathematical equations and solve them without confusion.
The 4-Step Word Problem Framework
1. Identify the Target and Given Ratio
Write down the labels and their exact numeric ratio (e.g. Cats : Dogs = 3 : 5).
2. Assign a Variable (x) to the "Unit Part"
Represent the quantities algebraically: Cats = 3x, and Dogs = 5x.
3. Formulate the Equation from Clues
Translate the problem's total, difference, or condition into an algebraic equation (e.g. 3x + 5x = Total).
4. Solve for x and Answer the Specific Question
Find the unit value x, then substitute it back to answer what the question specifically asks for.
Problem Type 1: Given a Total Amount
"A bakery sells 240 pastries. The ratio of croissants to muffins is 5 : 3. How many croissants were sold?"
- Ratio: Croissants : Muffins = 5 : 3 → Let Croissants = 5x, Muffins = 3x.
- Total equation: 5x + 3x = 240 → 8x = 240.
- Solve for x: x = 240 ÷ 8 = 30.
- Calculate Croissants: 5 × 30 = 150 croissants (Muffins = 3 × 30 = 90).
Problem Type 2: Given the Difference Between Parts
"In a garden, the ratio of roses to tulips is 7 : 4. There are 18 more roses than tulips. How many tulips are there?"
- Ratio: Roses = 7x, Tulips = 4x.
- Difference equation: 7x - 4x = 18 → 3x = 18.
- Solve for x: x = 18 ÷ 3 = 6.
- Calculate Tulips: 4 × 6 = 24 tulips (Roses = 7 × 6 = 42).