Question

solve for c in the proportion.
\frac{72}{84} = \frac{42}{c}

c = \square

Explanation:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{72}{84}=\frac{42}{c}\), cross - multiplying gives us \(72\times c = 84\times42\).

Step2: Calculate the right - hand side

First, calculate \(84\times42\). \(84\times42=(80 + 4)\times42=80\times42+4\times42 = 3360+168 = 3528\). So we have the equation \(72c = 3528\).

Step3: Solve for \(c\)

To solve for \(c\), divide both sides of the equation \(72c = 3528\) by 72. So \(c=\frac{3528}{72}\). Simplify \(\frac{3528}{72}\), we can divide numerator and denominator by 12 first: \(\frac{3528\div12}{72\div12}=\frac{294}{6}\), and then \(\frac{294\div6}{6\div6} = 49\).

Answer:

\(49\)