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]
[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]