To solve the given proportion:
[tex]\[
\frac{3}{5} = \frac{a + 5}{25}
\][/tex]
we will use cross-multiplication. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction. This will allow us to set up an equation without fractions.
Here's the step-by-step solution:
1. Set up the cross-multiplication:
[tex]\[
3 \times 25 = 5 \times (a + 5)
\][/tex]
2. Perform the multiplications:
[tex]\[
3 \times 25 = 75
\][/tex]
and
[tex]\[
5 \times (a + 5) = 5a + 25
\][/tex]
Now we have the equation:
[tex]\[
75 = 5a + 25
\][/tex]
3. Isolate the variable [tex]\(a\)[/tex]:
Subtract 25 from both sides of the equation:
[tex]\[
75 - 25 = 5a
\][/tex]
Simplifying the left side:
[tex]\[
50 = 5a
\][/tex]
4. Solve for [tex]\(a\)[/tex]:
Divide both sides by 5:
[tex]\[
\frac{50}{5} = a
\][/tex]
Simplifying, we get:
[tex]\[
a = 10
\][/tex]
So, the value of [tex]\(a\)[/tex] is:
[tex]\[
a = 10
\][/tex]
Therefore, the correct answer is [tex]\(a = 10\)[/tex].
