To determine the value of [tex]\( a \)[/tex] in the proportion [tex]\(\frac{3}{5} = \frac{a+5}{25}\)[/tex], we can solve this using the method of cross-multiplication.
Here are the step-by-step calculations:
1. Start with the given proportion:
[tex]\[
\frac{3}{5} = \frac{a+5}{25}
\][/tex]
2. Cross-multiply to eliminate the fractions:
[tex]\[
3 \times 25 = 5 \times (a + 5)
\][/tex]
3. Perform the multiplications:
[tex]\[
75 = 5a + 25
\][/tex]
4. Subtract 25 from both sides to isolate the term containing [tex]\( a \)[/tex]:
[tex]\[
75 - 25 = 5a
\][/tex]
[tex]\[
50 = 5a
\][/tex]
5. Divide both sides by 5 to solve for [tex]\( a \)[/tex]:
[tex]\[
50 \div 5 = a
\][/tex]
[tex]\[
a = 10
\][/tex]
So, the value of [tex]\( a \)[/tex] is [tex]\( \boxed{10} \)[/tex].
