Certainly! Let's solve the given proportion step-by-step:
We need to determine the number of days, [tex]\( x \)[/tex], required to complete the entire project if 17.5 days are needed to complete [tex]\(\frac{3}{8}\)[/tex] of the project. The given proportion is:
[tex]\[
\frac{17.5 \text{ days}}{\frac{3}{8} \text{ project}} = \frac{x \text{ days}}{1 \text{ project}}
\][/tex]
First, rewrite the proportion:
[tex]\[
\frac{17.5}{\frac{3}{8}} = \frac{x}{1}
\][/tex]
For convenience, we will simplify the left side of the equation. Dividing by a fraction is the same as multiplying by its reciprocal. Hence, we have:
[tex]\[
\frac{17.5}{\frac{3}{8}} = 17.5 \times \frac{8}{3}
\][/tex]
Next, calculate the product:
[tex]\[
17.5 \times \frac{8}{3} = 17.5 \times 2.6666666666666665
\][/tex]
Now perform the multiplication:
[tex]\[
17.5 \times 2.6666666666666665 \approx 46.666666666666664
\][/tex]
Thus, the number of days required to complete the entire project is:
[tex]\[
x = 46.666666666666664
\][/tex]
This means it will take approximately 46.67 days to complete the whole project if it takes 17.5 days to complete [tex]\(\frac{3}{8}\)[/tex] of it.
