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Anuta_ua [19.1K]
2 years ago
12

If the cost of an item increased by a percentage and decreased by the same percentage, what would that percentage be if the new

cost was 84% of the original?
Mathematics
1 answer:
Orlov [11]2 years ago
8 0

The percentage, if the new cost was 84% of the original is 40%

Let the cost of the item be x.

When the price increased by y%, the new price is:

New =x \times (1 + y\%)

When the price decreased by the same percentage (i.e. y%), the new price is:

New =x \times (1 + y\%) \times (1 - y\%)

The cost is said to be 84% of the original price.

So, we have:

x \times (1 + y\%) \times (1 - y\%) =84\% \times x

Divide both sides by x

(1 + y\%) \times (1 - y\%) =84\%

Apply the difference of two squares

1 - (y\%)^2 =84\% \\\\

Subtract 1 from both sides of the equation

- (y\%)^2 =-16\%

Cancel out the common factors

(y\%)^2 =16\%

Take the square root of both sides

y\% =0.4

Multiply both sides by 100

y =40

Hence, the percentage is 40%

Read more about percentage change at:

brainly.com/question/809966

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