Answer :
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].
[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].
