Let's solve the given proportion:
[tex]\[
\frac{3}{5} = \frac{a+5}{25}
\][/tex]
First, we will cross-multiply to eliminate the fractions. Cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the two products equal. This gives us:
[tex]\[
3 \cdot 25 = 5 \cdot (a+5)
\][/tex]
Next, we perform the multiplication on both sides:
[tex]\[
75 = 5(a + 5)
\][/tex]
Now, we distribute the 5 on the right-hand side:
[tex]\[
75 = 5a + 25
\][/tex]
We need to isolate [tex]\( a \)[/tex]. To do this, we first subtract 25 from both sides:
[tex]\[
75 - 25 = 5a
\][/tex]
This simplifies to:
[tex]\[
50 = 5a
\][/tex]
Next, we divide both sides by 5 to solve for [tex]\( a \)[/tex]:
[tex]\[
\frac{50}{5} = a
\][/tex]
This simplifies to:
[tex]\[
a = 10
\][/tex]
Therefore, the value of [tex]\( a \)[/tex] is [tex]\( 10 \)[/tex].
