To solve the problem of finding the antecedent in the ratio [tex]\(8:13\)[/tex] given that the consequent is [tex]\(91\)[/tex], we need to follow a step-by-step process applying the concept of ratios.
1. Understand the ratio: The ratio [tex]\(8:13\)[/tex] means for every 8 parts of the antecedent, there are 13 parts of the consequent.
2. Given Information: The consequent is provided as [tex]\(91\)[/tex].
3. Set up the proportion: We know that:
[tex]\[
\frac{\text{antecedent}}{\text{consequent}} = \frac{8}{13}
\][/tex]
Substituting the consequent:
[tex]\[
\frac{\text{antecedent}}{91} = \frac{8}{13}
\][/tex]
4. Solve for the antecedent: To find the antecedent, we need to isolate it by cross-multiplying:
[tex]\[
\text{antecedent} = \frac{8 \times 91}{13}
\][/tex]
5. Calculate the value:
[tex]\[
\text{antecedent} = \frac{728}{13} = 56
\][/tex]
Thus, the antecedent is [tex]\(56\)[/tex].
Therefore, the correct option is:
(c) 56
