Answer :
Certainly! Let's solve for \( C \) in the equation:
[tex]\[ \frac{5}{30} = \frac{3}{C} \][/tex]
### Step-by-Step Solution:
1. Cross-Multiplication:
To clear the fraction, we can use cross-multiplication. The concept of cross-multiplication states that if two fractions are equal, then the product of the numerator of one fraction and the denominator of the other fraction is equal to the product of the denominator of the first fraction and the numerator of the other. So, we write:
[tex]\[ 5 \cdot C = 3 \cdot 30 \][/tex]
2. Calculate the Products:
Now, we calculate the products on both sides of the equation.
[tex]\[ 5 \cdot C = 150 \][/tex]
3. Isolate \( C \):
To solve for \( C \), we need to isolate \( C \) on one side of the equation. We do this by dividing both sides of the equation by 5.
[tex]\[ C = \frac{150}{5} \][/tex]
4. Division:
Compute the division to find the value of \( C \).
[tex]\[ C = 30 \][/tex]
Thus, the solution is:
[tex]\[ C = 30 \][/tex]
So, the value of [tex]\( C \)[/tex] that satisfies the equation [tex]\(\frac{5}{30} = \frac{3}{C}\)[/tex] is [tex]\( C = 30 \)[/tex].
[tex]\[ \frac{5}{30} = \frac{3}{C} \][/tex]
### Step-by-Step Solution:
1. Cross-Multiplication:
To clear the fraction, we can use cross-multiplication. The concept of cross-multiplication states that if two fractions are equal, then the product of the numerator of one fraction and the denominator of the other fraction is equal to the product of the denominator of the first fraction and the numerator of the other. So, we write:
[tex]\[ 5 \cdot C = 3 \cdot 30 \][/tex]
2. Calculate the Products:
Now, we calculate the products on both sides of the equation.
[tex]\[ 5 \cdot C = 150 \][/tex]
3. Isolate \( C \):
To solve for \( C \), we need to isolate \( C \) on one side of the equation. We do this by dividing both sides of the equation by 5.
[tex]\[ C = \frac{150}{5} \][/tex]
4. Division:
Compute the division to find the value of \( C \).
[tex]\[ C = 30 \][/tex]
Thus, the solution is:
[tex]\[ C = 30 \][/tex]
So, the value of [tex]\( C \)[/tex] that satisfies the equation [tex]\(\frac{5}{30} = \frac{3}{C}\)[/tex] is [tex]\( C = 30 \)[/tex].
