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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]

Sagot :

GinnyAnswer
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].
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