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 :

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]