Solving Problems
3-4Using Equations to Solve Problems
Overview
Translate a real-world situation into an equation, solve it, and interpret the result.
Key ideas
- Define the variable clearly.
- Write one equation that captures the problem.
- Check your answer in the original context.
Worked examples
Example 1
Problem. A number doubled and increased by 7 is 31. Find it.
Solution. 2n + 7 = 31 → 2n = 24 → n = 12.
Practice
Try each one. Click Show answer when ready.
- 1.
5 more than 3 times a number is 26.
- 2.
If 8 is subtracted from twice a number, the result is 14.
- 3.
One third of a number, increased by 4, equals 10.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
A number divided by 3, minus 4, equals 5. Find the number.
- 2.
Twice a number plus 7 is the same as the number plus 15. Find the number.