use \( y \) to stand for the unknown. Show all your working: \( I \) am thinking of a number between 1 and 10 . When I add 2, then divide by 3 and multiply by 5 , I get 10. What is the number? \[ \begin{aligned} (v+\square) \div \square & =10 \\ 1+\square \div \square \div \square & =10 \div 5 \\ y+\square \square \square \square \square & =\square \square \square \square \square \\ y+\square & =\square \square \square \square \square \end{aligned} \]

Certainly! Let's solve the problem step-by-step using algebra, with \( y \) representing the unknown number. ### **Problem Statement** You are thinking of a number between 1 and 10. When you add 2 to this number, divide the result by 3, and then multiply by 5, you obtain 10. What is the number? ### **Step-by-Step Solution** 1. **Define the Variable** Let \( y \) be the unknown number. 2. **Translate the Problem into an Equation** According to the problem: - Add 2 to the number: \( y + 2 \) - Divide the result by 3: \( \frac{y + 2}{3} \) - Multiply by 5: \( \frac{y + 2}{3} \times 5 \) This final expression is equal to 10: \[ \frac{(y + 2)}{3} \times 5 = 10 \] 3. **Simplify the Equation** Start by simplifying the left side of the equation: \[ \frac{5(y + 2)}{3} = 10 \] This simplifies to: \[ \frac{5y + 10}{3} = 10 \] 4. **Eliminate the Fraction** Multiply both sides of the equation by 3 to eliminate the denominator: \[ 5y + 10 = 30 \] 5. **Isolate the Variable Term** Subtract 10 from both sides to isolate the term containing \( y \): \[ 5y = 20 \] 6. **Solve for \( y \)** Divide both sides by 5 to solve for \( y \): \[ y = 4 \] ### **Conclusion** The number you are thinking of is **4**. ### **Verification** Let's verify the solution to ensure it's correct. 1. **Add 2 to the number:** \[ 4 + 2 = 6 \] 2. **Divide by 3:** \[ \frac{6}{3} = 2 \] 3. **Multiply by 5:** \[ 2 \times 5 = 10 \] This matches the given condition, confirming that \( y = 4 \) is indeed the correct solution.