To find out the total number of managers at Antares Corporation, given that 3/7 of the managers are female and there are 42 female managers, follow these steps:
1. Understand the proportion: We are told that 3/7 of the managers are female.
2. Set up the equation: Let the total number of managers be [tex]\( x \)[/tex]. According to the problem, 3/7 of [tex]\( x \)[/tex] equals 42. So we set up the equation:
[tex]\[
\frac{3}{7} \times x = 42
\][/tex]
3. Solve for [tex]\( x \)[/tex]: To find [tex]\( x \)[/tex], isolate it by performing the following steps:
[tex]\[
x = \frac{42 \times 7}{3}
\][/tex]
4. Calculate the result:
[tex]\[
x = 98
\][/tex]
Therefore, the total number of managers at Antares Corporation is [tex]\( \boxed{98} \)[/tex].
