To determine the original value from which [tex]\( 135\% \)[/tex] corresponds to [tex]\( 3645 \)[/tex] kilograms, we follow these steps:
1. Let the original value be [tex]\( x \)[/tex] kilograms.
2. According to the problem, [tex]\( 135\% \)[/tex] of this original value [tex]\( x \)[/tex] is [tex]\( 3645 \)[/tex] kg. Mathematically, this is represented as:
[tex]\[
135\% \times x = 3645 \text{ kg}
\][/tex]
3. We know that [tex]\( 135\% \)[/tex] can be written as a fraction:
[tex]\[
135\% = \frac{135}{100} = 1.35
\][/tex]
4. Substituting [tex]\( 1.35 \)[/tex] for [tex]\( 135\% \)[/tex] in the equation gives:
[tex]\[
1.35 \times x = 3645 \text{ kg}
\][/tex]
5. To solve for [tex]\( x \)[/tex], divide both sides of the equation by [tex]\( 1.35 \)[/tex]:
[tex]\[
x = \frac{3645 \text{ kg}}{1.35}
\][/tex]
6. After performing the division, we find:
[tex]\[
x \approx 2700 \text{ kg}
\][/tex]
Thus, the original value is [tex]\( 2700 \)[/tex] kilograms.
