Toby thinks of a number less than 15. He divides it by 2 and then adds 4. He then divides the result by 3. His answer is 3.5. What number did Toby start with?
Answer (2)
Let x be the number Toby started with.
Write the equation: 3 2 x + 4 = 3.5 .
Multiply both sides by 3: 2 x + 4 = 10.5 .
Subtract 4 from both sides: 2 x = 6.5 .
Multiply both sides by 2: x = 13 .
The number Toby started with is 13 .
Explanation
Problem Analysis Let's analyze the problem. Toby starts with a number (let's call it x ), performs a series of operations, and ends up with 3.5. We need to reverse these operations to find the original number.
Setting up the Equation The operations Toby performs are:
Divide by 2: x /2
Add 4: x /2 + 4
Divide by 3: ( x /2 + 4 ) /3 The final result is 3.5, so we can write the equation:
The Equation 3 2 x + 4 = 3.5
Reversing the Operations - Step 1 To solve for x , we need to reverse the operations. First, multiply both sides of the equation by 3:
Multiply by 3 2 x + 4 = 3.5 × 3 2 x + 4 = 10.5
Reversing the Operations - Step 2 Next, subtract 4 from both sides:
Subtract 4 2 x = 10.5 − 4 2 x = 6.5
Reversing the Operations - Step 3 Finally, multiply both sides by 2 to isolate x :
Multiply by 2 x = 6.5 × 2 x = 13
Final Answer So, the number Toby started with is 13.
Examples
Imagine you're baking a cake and need to adjust the recipe because you only want a portion of the original cake. If the original recipe calls for a certain amount of flour, and you decide to halve the recipe and then add a bit more for extra fluffiness, this problem is similar to figuring out how much flour you started with based on the final amount and the adjustments you made. Understanding how to reverse the operations helps you accurately adjust recipes and get the desired outcome.
Toby started with the number 13. We arrived at this by setting up an equation based on the operations he performed and solving for the original number. This value is indeed less than 15, satisfying the conditions of the problem.
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