Applications and Problem Solving
1-7A Problem Solving Plan
Overview
A reliable plan: READ, PLAN, SOLVE, CHECK. Restate the problem, choose a variable, write an equation, solve, and verify.
Key ideas
- Always re-read the problem after solving.
- Check that your answer makes sense in context.
- Include units when reporting an answer.
Worked examples
Example 1
Problem. Maria is 4 years older than her brother. Their ages add to 24. How old is each?
Solution. Let b = brother. Maria = b + 4. b + (b + 4) = 24 → 2b = 20 → b = 10, Maria = 14.
Practice
Try each one. Click Show answer when ready.
- 1.
Two consecutive numbers sum to 47. Find them.
- 2.
A pen costs $2 more than a pencil. Together they cost $5. Find each price.
- 3.
Three times a number, less 7, is 20. Find the number.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
A number plus twice the number plus 5 equals 26. Use the problem-solving plan to find the number.
- 2.
The sum of three consecutive even integers is 84. What are the integers?