To find the value of the number [tex]\(X\)[/tex] given that [tex]\(\frac{5}{7}\)[/tex] of [tex]\(X\)[/tex] is equal to [tex]\(\frac{4}{5}\)[/tex] of another number [tex]\(Y\)[/tex] and [tex]\(Y = 75\)[/tex], we can follow these steps:
1. Write the equation based on the given relationship:
[tex]\[
\frac{5}{7} X = \frac{4}{5} Y
\][/tex]
2. Substitute [tex]\(Y = 75\)[/tex] into the equation:
[tex]\[
\frac{5}{7} X = \frac{4}{5} \cdot 75
\][/tex]
3. Calculate [tex]\(\frac{4}{5} \cdot 75\)[/tex]:
[tex]\[
\frac{4}{5} \cdot 75 = 4 \cdot 15 = 60
\][/tex]
4. So, the equation simplifies to:
[tex]\[
\frac{5}{7} X = 60
\][/tex]
5. Solve for [tex]\(X\)[/tex] by isolating [tex]\(X\)[/tex]:
[tex]\[
X = 60 \cdot \frac{7}{5}
\][/tex]
6. Calculate [tex]\(60 \cdot \frac{7}{5}\)[/tex]:
[tex]\[
60 \cdot \frac{7}{5} = 60 \cdot 1.4 = 84
\][/tex]
So, the value of the number [tex]\(X\)[/tex] is [tex]\(\boxed{84}\)[/tex].
