Ratio Word Problems

Real-world ratio problems rarely announce themselves as “ratio questions” – they show up disguised as recipes, paint mixes, map distances, and shared costs. Solving them well means first identifying the ratio hidden in the words, then applying whichever skill from this section fits: scaling with a ratio table, splitting a part-to-part comparison, or finding a part-to-whole fraction.

A Step-by-Step Approach

1. Identify the ratio and what it compares. 2. Work out the scale factor from any given actual amount. 3. Apply that same scale factor to find the unknown quantity.

A squash drink is made from concentrate and water in the ratio 1:4. How much water is needed for 250 ml of concentrate?

Scale factor = 250 ÷ 1 = 250. Water needed = 4 × 250 = 1,000 ml.

A Mixing Problem

Grey paint is made from black and white paint in the ratio 2:5. How much black paint is needed to make 7 litres of grey paint?

Total parts = 2 + 5 = 7. Each part = 7 litres ÷ 7 = 1 litre. Black paint = 2 × 1 = 2 litres.

Real-Life Application

Cooking: adjusting recipes for a different number of servings.
DIY and construction: mixing cement, paint, or fertiliser correctly.
Sharing costs: splitting a bill fairly based on usage.

Key Takeaways

The first step in any ratio word problem is identifying exactly what the ratio compares.
Finding the scale factor from a known quantity unlocks the rest of the problem.
This closes out the pure ratio skills of this section – proportion, covered next, formalises the same idea as an equation.

Practice: Ratio Word Problems

Ratio Word Problem: Recipe