Points to Remember:
- The problem involves a series of arithmetic operations on an unknown number.
- We need to translate the word problem into an algebraic equation.
- Solving the equation will reveal the original number Anita thought of.
Introduction:
This question is a classic example of a word problem in algebra. It tests the ability to translate a verbal description of a mathematical process into a symbolic equation and then solve for the unknown variable. Word problems are crucial for developing problem-solving skills and applying mathematical concepts to real-world scenarios. This particular problem involves a single unknown variable, making it solvable using basic algebraic techniques.
Body:
1. Translating the Word Problem into an Equation:
Let’s represent the number Anita thought of as ‘x’. The problem can be broken down step-by-step:
- Anita subtracts 5/2 from her number: x – 5/2
- She multiplies the result by 8: 8(x – 5/2)
- The result is 3 times the original number: 8(x – 5/2) = 3x
2. Solving the Equation:
Now we solve the equation for x:
8(x – 5/2) = 3x
8x – 20 = 3x
8x – 3x = 20
5x = 20
x = 20/5
x = 4
3. Verification:
Let’s check our answer:
- Anita’s number: 4
- Subtracts 5/2: 4 – 5/2 = 3/2
- Multiplies by 8: 8 * (3/2) = 12
- 12 is 3 times the original number (4 * 3 = 12). The solution is correct.
Conclusion:
The number Anita thought of is 4. We arrived at this solution by carefully translating the word problem into an algebraic equation, simplifying the equation, and solving for the unknown variable. Verifying the solution ensures accuracy. This problem highlights the importance of translating real-world scenarios into mathematical models, a fundamental skill in various fields, from engineering and finance to computer science and data analysis. The ability to accurately translate and solve such equations is crucial for developing strong analytical and problem-solving skills, essential for holistic development and success in many academic and professional pursuits.