Year 8: I think of a number

Understanding the Challenge

This challenge tests your ability to use addition, subtraction, multiplication, and division to solve a problem. You are given a prompt, "I think of a number," and you need to figure out the number based on the operations presented.

Key Steps

1. Understand the Prompt: The phrase "I think of a number" means someone has chosen a single number.
2. Define a Variable: Let's use a letter, like 'x', to represent the unknown number.
3. Set Up Equations: You will usually be given multiple equations using 'x'. Each equation represents a relationship between 'x' and other numbers.
4. Solve the Equations: Use the order of operations (BODMAS/PEMDAS) to solve for 'x' in each equation.
5. Check Your Answer: Substitute your solution back into the original equations to ensure it makes them true.

Example

Suppose you are told: 'I think of a number. I double it, then add 5. The result is 15.'

Let 'x' be the number.

Equation: 2x + 5 = 15

Subtract 5 from both sides: 2x = 10

Divide both sides by 2: x = 5

Therefore, the number is 5.