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Math  /  Algebra

Question5.) If I decrease a number by 62%62 \%, what %\% do you need to apply to the result to get back to your original number?

Studdy Solution

STEP 1

Assumptions
1. Let the original number be denoted as x x .
2. The number is decreased by 62% 62\% .
3. We need to find the percentage increase required to return to the original number x x .

STEP 2

Calculate the new number after decreasing the original number by 62% 62\% .
The decrease in the number is given by:
Decrease=x×62%=x×0.62 \text{Decrease} = x \times 62\% = x \times 0.62

STEP 3

Subtract the decrease from the original number to find the new number.
New number=x−(x×0.62)=x×(1−0.62)=x×0.38 \text{New number} = x - (x \times 0.62) = x \times (1 - 0.62) = x \times 0.38

STEP 4

Let y y be the percentage increase needed to return to the original number. We need to find y y such that:
New number×(1+y)=x \text{New number} \times (1 + y) = x

STEP 5

Substitute the expression for the new number from STEP_3 into the equation.
(x×0.38)×(1+y)=x (x \times 0.38) \times (1 + y) = x

STEP 6

Divide both sides of the equation by x x to isolate the term with y y .
0.38×(1+y)=1 0.38 \times (1 + y) = 1

STEP 7

Solve for y y by dividing both sides by 0.38 0.38 .
1+y=10.38 1 + y = \frac{1}{0.38}

STEP 8

Calculate 10.38 \frac{1}{0.38} .
10.38≈2.6316 \frac{1}{0.38} \approx 2.6316

STEP 9

Subtract 1 from both sides to solve for y y .
y=2.6316−1 y = 2.6316 - 1

STEP 10

Calculate y y .
y≈1.6316 y \approx 1.6316

STEP 11

Convert y y to a percentage by multiplying by 100.
y≈1.6316×100=163.16% y \approx 1.6316 \times 100 = 163.16\%
To return to the original number after a 62% 62\% decrease, you need to apply an increase of approximately 163.16% 163.16\% .

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