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Question

$$ 1< $$ If you copy a page on a machine at $$ 50 \% $$, you should get a similar copy of the page. What is the corresponding setting to obtain the original from the copy? The corresponding setting to obtain the original from the copy is $$ \square \% $$. (Simplify your answer. Type an integer, proper fraction, or mixed number.)

UpStudy AI · Accepted Answer

To find the corresponding setting to obtain the original from a copy that was made at $$ 50\% $$, we can set up the relationship between the copy and the original.

Let:
- $$ O $$ be the original size,
- $$ C $$ be the copy size.

From the problem, we know that when the original is copied at $$ 50\% $$, the size of the copy is:

$$
C = 0.5 \times O
$$

To find the percentage setting needed to enlarge the copy back to the original size, we need to determine what percentage of the copy corresponds to the original size. We can express this as:

$$
O = x \times C
$$

Substituting $$ C $$ from the first equation into this equation gives:

$$
O = x \times (0.5 \times O)
$$

Now, we can solve for $$ x $$:

$$
O = 0.5x \times O
$$

Assuming $$ O \neq 0 $$, we can divide both sides by $$ O $$:

$$
1 = 0.5x
$$

Now, solving for $$ x $$:

$$
x = \frac{1}{0.5} = 2
$$

To express this as a percentage, we multiply by $$ 100\% $$:

$$
x = 2 \times 100\% = 200\%
$$

Thus, the corresponding setting to obtain the original from the copy is $$ 200\% $$.

The final answer is:

$$
\boxed{200}
$$
The corresponding setting to obtain the original from the copy is $$ 200\% $$.

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