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A number is multiplied by 5. Then, 40 is subtracted from the product. The result obtained is then
multiplied by 2 and 50 subtracted from the product so obtained. The answer is a two-digit number.
What is the largest integer that can be used to get a two-digit number as the answer?
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Most Upvoted Answer
A number is multiplied by 5. Then, 40 is subtracted from the product. ...
Analysis:
To find the largest integer that can be used to get a two-digit number as the answer after performing the given operations, we need to work backwards. Starting from the final step, we will reverse engineer the process to determine the largest integer that results in a two-digit answer.

Reverse Engineering:
1. Let the final two-digit number be represented as \(x\).
2. Adding 50 to this number gives \(x + 50\).
3. Dividing this number by 2 results in \(\frac{x + 50}{2}\).
4. Adding 40 to this number gives \(\frac{x + 50}{2} + 40\).
5. Finally, multiplying this number by 5 gives \(5(\frac{x + 50}{2} + 40)\).

Calculations:
To ensure that the final result is a two-digit number, we can set up the following inequality:
\[10 \leq 5(\frac{x + 50}{2} + 40) < />
Solving this inequality will give the range of values for \(x\), and the largest integer within this range will be the answer.

Conclusion:
By solving the inequality obtained from reverse engineering the given operations, we can determine the largest integer that can be used to get a two-digit number as the answer. This approach ensures a systematic and logical method to arrive at the correct solution.
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A number is multiplied by 5. Then, 40 is subtracted from the product. The result obtained is then multiplied by 2 and 50 subtracted from the product so obtained. The answer is a two-digit number. What is the largest integer that can be used to get a two-digit number as the answer?
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