Let's solve the equation step-by-step:
[tex]\[
\frac{30}{2c} = \frac{20}{12}
\][/tex]
1. Simplify the right side of the equation:
[tex]\[
\frac{20}{12} = \frac{20 \div 4}{12 \div 4} = \frac{5}{3}
\][/tex]
So the equation now looks like this:
[tex]\[
\frac{30}{2c} = \frac{5}{3}
\][/tex]
2. To eliminate the fractions, we can cross-multiply. Cross-multiplication will give us:
[tex]\[
30 \times 3 = 5 \times (2c)
\][/tex]
Simplify both sides:
[tex]\[
90 = 10c
\][/tex]
3. Solve for \( c \):
[tex]\[
c = \frac{90}{10}
\][/tex]
[tex]\[
c = 9
\][/tex]
So the solution to the equation \(\frac{30}{2c} = \frac{20}{12}\) is \( c = 9 \).
To ensure our solution is correct, we can substitute \( c \) back into the original equation and check:
[tex]\[
\frac{30}{2 \times 9} = \frac{30}{18} = \frac{5}{3} = \frac{20}{12}
\][/tex]
This confirms the solution \( c = 9 \) is correct.
Additionally, the simplified right side of the equation was \(\frac{5}{3} \approx 1.6667\). Therefore, the solution yields:
\(
\left(1.6667, 9\right)
\).
