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2020 is added to a mystery number. The result is multiplied by 55. After that 4343 is subtracted. The final value is 352352. What was the mystery number at the beginning?

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Full solution

Q. 2020 is added to a mystery number. The result is multiplied by 55. After that 4343 is subtracted. The final value is 352352. What was the mystery number at the beginning?
  1. Define Mystery Number: Let xx be the mystery number.\newlineFirst, add 2020 to xx: x+20x + 20.
  2. Perform Addition: Next, multiply the result by 55: 5(x+20)5(x + 20).
  3. Perform Multiplication: Then, subtract 4343 from the result: 5(x+20)−435(x + 20) - 43.
  4. Perform Subtraction: The final value is given as 352352, so set the expression equal to 352352: 5(x+20)−43=3525(x + 20) - 43 = 352.
  5. Set Equation Equal to 352352: Now, solve for xx. Start by adding 4343 to both sides: 5(x+20)=352+435(x + 20) = 352 + 43.
  6. Add 4343 to Both Sides: Calculate the right side: 5(x+20)=3955(x + 20) = 395.
  7. Divide by 55: Divide both sides by 55 to isolate (x+20)(x + 20): (x+20)=3955(x + 20) = \frac{395}{5}.
  8. Isolate xx: Calculate the division: (x+20)=79(x + 20) = 79.
  9. Subtract 2020: Finally, subtract 2020 from both sides to solve for xx: x=79−20x = 79 - 20.
  10. Calculate Final Value: Calculate the subtraction: x=59x = 59.

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