Lesson 53: Ratio Word Problems

New Concept

Math concepts are introduced incrementally. Simple tools you master now, like ratio boxes, will be expanded to solve more complex problems in later lessons.

What’s next

Our journey begins with a foundational skill. Next, you will see worked examples on how to use ratio boxes to solve word problems.

Property

A ratio box organizes information into two columns (Ratio, Actual Count) and rows for the groups being compared, like parrots and macaws.

Examples

Parrots to macaws is 3 to 5. With 45 parrots: $\frac{3}{5} = \frac{45}{m}$, so $m=75$ macaws. Boys to girls is 5 to 4. With 200 girls: $\frac{5}{4} = \frac{B}{200}$, so $B=250$ boys.

Explanation

Think of a ratio box as a cheat sheet for word problems. It helps you sort the 'ratio' numbers from the 'actual count' numbers, making it a piece of cake to write a proportion correctly.

Property

A proportion is a statement that two ratios are equal, written as an equation like $\frac{a}{b} = \frac{c}{d}$.

Examples

From $\frac{5}{4} = \frac{B}{200}$, we get $4B = 5 \cdot 200$, so $B=250$. From girl-boy ratio 9 to 7 with 63 girls: $\frac{9}{7} = \frac{63}{B}$, giving $9B = 441$, so $B=49$.

Explanation

Solving is a cross-multiplication adventure! Multiply diagonally across the equals sign to form a simple equation. This is the key action step where you finally reveal the unknown number in your problem.