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Math  /  Algebra

Question12. A number is decreased by 50%50 \%, and the resulting number is then increased by 300%300 \%. The original number is what percentage of the final number? F. 20%20 \% G. 25%25 \% H. 40%40 \% J. 50%50 \% K. 400%400 \% Entrance Tickot

Studdy Solution

STEP 1

1. Let the original number be denoted as x x .
2. The original number is decreased by 50% 50\% .
3. The resulting number is then increased by 300% 300\% .
4. We need to find what percentage the original number is of the final number.

STEP 2

1. Calculate the number after the 50% 50\% decrease.
2. Calculate the number after the 300% 300\% increase.
3. Determine the percentage of the original number relative to the final number.

STEP 3

Calculate the number after the 50% 50\% decrease.
The number after a 50% 50\% decrease is:
x−0.5x=0.5x x - 0.5x = 0.5x

STEP 4

Calculate the number after the 300% 300\% increase.
The number after a 300% 300\% increase is:
0.5x+3×0.5x=0.5x+1.5x=2x 0.5x + 3 \times 0.5x = 0.5x + 1.5x = 2x

STEP 5

Determine the percentage of the original number relative to the final number.
The original number x x is what percentage of the final number 2x 2x ?
Percentage=(x2x)×100%=12×100%=50% \text{Percentage} = \left( \frac{x}{2x} \right) \times 100\% = \frac{1}{2} \times 100\% = 50\%
The original number is:
50% \boxed{50\%}

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