Age Ratio Problem: David and Tom

mediumGrade 5-7age ratio

The Problem

David is 36 years old. David is twice as old as Tom. How old is Tom?

Answer:

18 years old

Key Information

  • David is 36 years old
  • David is twice as old as Tom

Formula

Age₁ = ratio × Age₂

Step-by-Step Solution

1

Identify the relationship

David is twice as old as Tom
2

Set up equation

David's age = 2 × Tom's age
3

Substitute known value

36 = 2 × Tom's age
4

Solve for unknown age

Tom's age = 36 ÷ 2
5

Calculate

36 ÷ 2 = 18
6

Final answer

Tom is 18 years old

Common Mistakes to Avoid

  • Multiplying instead of dividing
  • Using the wrong person's age

Helpful Tips

  • When someone is "twice as old," divide by 2 to find the younger age
  • Check your answer by multiplying back

Real-World Application

Ratio problems help understand proportional relationships between ages.

Universal Word Problem Strategy

Use this 5-step strategy for any word problem you encounter:

R

Read Carefully

Read the entire problem at least twice. Don't rush - understanding is key. Identify what question is being asked.

I

Identify Information

List all the given facts, numbers, and what you need to find. Underline or highlight key data.

S

Set Up the Equation

Translate words into math. Use variables for unknowns. Choose the right formula or create an equation.

E

Execute the Solution

Solve step by step. Show your work. Keep calculations organized and double-check arithmetic.

S

Sanity Check

Does your answer make sense in context? Check units. Re-read the question to ensure you answered what was asked.

Remember: R-I-S-E-S = Read, Identify, Set up, Execute, Sanity check

Tips for Age Problems

Recognize Patterns

Age problems often involve time relationships (years ago, years from now). Set up equations comparing ages at different times.

Define Variables Clearly

Write out what each variable represents. For example: "Let x = current age" is clearer than just "x = age." This prevents confusion when solving.

Work Backwards to Check

Once you have an answer, plug it back into the original problem (not just your equation). Does it satisfy all the conditions stated?

Draw It Out

Diagrams, tables, and visual representations help organize information and reveal relationships that aren't obvious from text alone.

Frequently Asked Questions

What is the answer to this problem?▼
The answer is 18 years old. See the step-by-step solution above for the complete explanation of how to arrive at this answer.
How do you approach age problems?▼
First, read carefully to understand what's being asked. Then identify all given information and what you need to find. Set up equations based on the relationships described, solve step by step, and verify your answer makes sense in the real-world context.
What are the key steps to solving word problems?▼
Use the R-I-S-E-S method: Read the problem carefully, Identify known information,Set up equations, Execute the solution, and Sanity check your answer. This systematic approach works for any type of word problem.
Why are word problems important?▼
Word problems connect math to real life. They develop critical thinking, reading comprehension, and problem-solving skills that are essential in careers like engineering, science, medicine, finance, and technology. They also appear frequently on standardized tests like SAT and ACT.
What's the most common mistake in word problems?▼
The most common mistake is not reading carefully enough. Many students rush and miss key details, or answer a different question than what was asked. Always re-read the problem after solving to ensure your answer addresses what was specifically asked.
How can I get better at word problems?▼
Practice regularly with different types of problems. Start with easier ones and progress to harder ones. Always write out your work step by step. Review mistakes to understand where you went wrong. Learn to recognize common problem patterns. With consistent practice, word problems become much easier!

Related Topics:

ageratiodivisionword problems

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