To determine the value of \( a \) in the proportion given:
[tex]\[
\frac{3}{5} = \frac{a+5}{25}
\][/tex]
we use the property of proportions, which states that if \(\frac{a}{b} = \frac{c}{d}\), then \(a \cdot d = b \cdot c\).
First, we cross-multiply the terms of the proportion:
[tex]\[
3 \cdot 25 = 5 \cdot (a + 5)
\][/tex]
This simplifies to:
[tex]\[
75 = 5 \cdot (a + 5)
\][/tex]
Next, distribute the 5 on the right side:
[tex]\[
75 = 5a + 25
\][/tex]
To isolate the variable \( a \), subtract 25 from both sides of the equation:
[tex]\[
75 - 25 = 5a
\][/tex]
Simplify the left side:
[tex]\[
50 = 5a
\][/tex]
Finally, solve for \( a \) by dividing both sides by 5:
[tex]\[
a = \frac{50}{5}
\][/tex]
This simplifies to:
[tex]\[
a = 10
\][/tex]
So, the correct value of \( a \) is:
[tex]\[
a = 10
\][/tex]
Thus, the answer is:
[tex]\[
a = 10
\][/tex]
