Use proportional reasoning to determine the value of [tex]a[/tex] in the proportion shown below.

[tex]\[ \frac{3}{5} = \frac{a+5}{25} \][/tex]

A. [tex]a=1[/tex]

B. [tex]a=25[/tex]

C. [tex]a=10[/tex]

D. [tex]a=15[/tex]



Answer :

Let's determine the value of [tex]\( a \)[/tex] using the proportion given:

[tex]\[ \frac{3}{5} = \frac{a+5}{25} \][/tex]

To solve this proportion, we will use cross-multiplication. Cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal to each other. This gives us:

[tex]\[ 3 \cdot 25 = 5 \cdot (a + 5) \][/tex]

Now, let's perform the multiplication:

[tex]\[ 75 = 5 \cdot (a + 5) \][/tex]

Next, we need to distribute the 5 on the right-hand side to both terms inside the parentheses:

[tex]\[ 75 = 5a + 25 \][/tex]

Now, we will isolate [tex]\( a \)[/tex] by first subtracting 25 from both sides of the equation:

[tex]\[ 75 - 25 = 5a \\ 50 = 5a \][/tex]

Finally, we solve for [tex]\( a \)[/tex] by dividing both sides of the equation by 5:

[tex]\[ a = \frac{50}{5} \\ a = 10 \][/tex]

So, the value of [tex]\( a \)[/tex] is [tex]\( \boxed{10} \)[/tex].