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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][tex]$a = 10$[/tex][/tex]
D. [tex]$a = 15$[/tex]

Sagot :

GinnyAnsweridn
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].
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