To solve for the value of [tex]\(\frac{5}{7}\)[/tex] of the number, given that [tex]\(\frac{3}{7}\)[/tex] of the number is 33.75, we follow these steps:
1. Finding the Original Number:
- We know that [tex]\(\frac{3}{7}\)[/tex] of the number equals 33.75.
- Let the original number be [tex]\(x\)[/tex]. According to the problem, [tex]\(\frac{3}{7}x = 33.75\)[/tex].
- To find the original number [tex]\(x\)[/tex], solve for [tex]\(x\)[/tex]:
[tex]\[
x = 33.75 \times \frac{7}{3}
\][/tex]
- When you multiply 33.75 by [tex]\(\frac{7}{3}\)[/tex], you get the original number, [tex]\(x = 78.75\)[/tex].
2. Finding [tex]\(\frac{5}{7}\)[/tex] of the Original Number:
- Now that we have the original number [tex]\(x = 78.75\)[/tex], we need to find what [tex]\(\frac{5}{7}\)[/tex] of this number is:
[tex]\[
\frac{5}{7} \times 78.75
\][/tex]
- When you calculate [tex]\(\frac{5}{7} \times 78.75\)[/tex], you get 56.25.
Therefore, the value of [tex]\(\frac{5}{7}\)[/tex] of the original number is [tex]\( \boxed{56.25} \)[/tex].
