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? \[ \begin{aligned} (v+\square) \div \square & =10 \\ 1+\square \div \square \div \square & =10 \div 5 \\ y+\square \square \square \square \square & =\square \square \square \square \square \\ y+\square & =\square \square \square \square \square \end{aligned} \]
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Let's solve the problem step by step using \( y \) as the unknown number. 1. Start with the number \( y \) (the unknown) 2. According to your statement: \[ \frac{(y + 2)}{3} \times 5 = 10 \] 3. To simplify, start by dividing both sides by 5: \[ \frac{(y + 2)}{3} = \frac{10}{5} \] \[ \frac{(y + 2)}{3} = 2 \] 4. Now, multiply both sides by 3 to eliminate the denominator: \[ y + 2 = 2 \times 3 \] \[ y + 2 = 6 \] 5. Subtract 2 from both sides to solve for \( y \): \[ y = 6 - 2 \] \[ y = 4 \] So the number I was thinking of is \( 4 \). Now let's add some extra knowledge! When it comes to solving simple equations like this, it's a great idea to visualize the operations you're performing! Imagine you have a box (your number \( y \)). When you add 2, you're placing another box next to it. Then, you’re dividing that total box into three equal parts. It’s like sharing candies equally among friends! If you ever find yourself stuck on a problem, remember that breaking it down into smaller parts can help a lot! Don’t hesitate to write out each step, and double-check your arithmetic. It's easy to lose track of a minus sign or a multiplication—math has its own sneaky little tricks!
