Ratio Word Problems

In this lesson, we will explore how to solve ratio word problems. Ratios compare two or more quantities, showing the relative sizes of two or more values. Understanding ratios is crucial for solving various problems in the SAT Math section.

Explanation

A ratio is a relationship between two numbers indicating how many times the first number contains the second. It can be expressed in several forms: as a fraction, with a colon, or in words. For example, the ratio of 3 to 2 can be written as $\frac{3}{2}$, $3:2$, or "3 to 2".

Worked Example

Problem: The ratio of cats to dogs in a shelter is 4:5. If there are 20 cats, how many dogs are there?

1. Let the number of dogs be $d$.
2. The ratio of cats to dogs is given as $\frac{cats}{dogs} = \frac{4}{5}$.
3. We know there are 20 cats, so we can substitute: $\frac{20}{d} = \frac{4}{5}$.
4. Cross-multiply to solve for $d$: $20 \cdot 5 = 4 \cdot d$.
5. This simplifies to $100 = 4d$.
6. Divide both sides by 4: $d = \frac{100}{4} = 25$.

Answer: There are 25 dogs in the shelter.

Key Questions

• What is the ratio of 6 to 9 expressed in simplest form?
• If the ratio of boys to girls in a class is 2:3 and there are 12 boys, how many girls are there?
• A recipe calls for a ratio of 1:4 of sugar to flour. If you use 2 cups of sugar, how much flour do you need?
• If the ratio of apples to oranges is 3:2 and there are 15 apples, how many oranges are there?

Keywords

• Ratio
• Proportion
• Compare
• Quantities
• Cross-multiplication