Ten is added to a certain number. The resulting sum is multiplied by 7, the product is divided by 5, and then 5 is subtracted from the quotient. The final result is half of 88. What is the original number?

Introduction / Context:
This problem is a typical algebraic puzzle based on a sequence of operations. Starting from an unknown number, we perform several steps and are given the final result. The task is to reverse these steps using algebra and solve for the original number. Such questions test the ability to translate verbal descriptions into equations.

Given Data / Assumptions:
Let the original number be N.Ten is added to N.The sum is multiplied by 7.The product is divided by 5.Five is subtracted from the quotient.The final result equals half of 88, which is 44.

Concept / Approach:
We convert the verbal process into a single algebraic expression in N and set it equal to 44. Then we solve the resulting linear equation step by step. It is important to keep the order of operations exactly as described and to simplify carefully.

Step-by-Step Solution:
Step 1: Start with N.Step 2: Add 10 to get N + 10.Step 3: Multiply this sum by 7 to get 7(N + 10).Step 4: Divide the product by 5 to get [7(N + 10)] / 5.Step 5: Subtract 5 from this quotient: [7(N + 10)] / 5 − 5.Step 6: According to the problem, this expression equals half of 88, which is 44.Step 7: Set up the equation: [7(N + 10)] / 5 − 5 = 44.Step 8: Add 5 to both sides: [7(N + 10)] / 5 = 49.Step 9: Multiply both sides by 5: 7(N + 10) = 49 × 5 = 245.Step 10: Divide both sides by 7: N + 10 = 245 / 7 = 35.Step 11: Subtract 10 from both sides: N = 35 − 10 = 25.

Verification / Alternative check:
Check the answer by following the operations with N = 25. Add 10 to get 35. Multiply by 7 to get 245. Divide by 5 to obtain 49. Subtract 5 to get 44, which is exactly half of 88. This confirms that the original number 25 fits the described process.

Why Other Options Are Wrong:
For N = 20, the process gives ((20 + 10) × 7) / 5 − 5 = (30 × 7) / 5 − 5 = 210 / 5 − 5 = 42 − 5 = 37, not 44. For N = 21, we get ((21 + 10) × 7) / 5 − 5 = 217 / 5 − 5, which is not an integer and not 44. For N = 30, the result is ((30 + 10) × 7) / 5 − 5 = 280 / 5 − 5 = 56 − 5 = 51. None match the required outcome.

Common Pitfalls:
Some learners reverse the order of operations or incorrectly handle the division and subtraction steps. Others may forget to convert half of 88 to 44 before forming the equation. Carefully writing the sequence as nested algebraic operations prevents such errors.

Final Answer:
The original number is 25.