An inventory manager uses the proportion $\frac{n}{n+14} = \frac{5}{7}$ to determine the number of standard shipping containers ($n$) needed out of the total shipment ($n+14$) to maintain a specific cost ratio. Arrange the following algebraic steps in the correct sequence to solve for $n$.

A project manager is analyzing the ratio of completed tasks ($n$) to total assigned tasks ($n+14$) for a corporate training module. This relationship is represented by the proportion $\frac{n}{n+14} = \frac{5}{7}$. Based on the standard procedure for solving this equation, what is the first step taken to eliminate the fractions?

A warehouse manager uses the equation $\frac{n}{n+14} = \frac{5}{7}$ to determine the number of high-priority shipments ($n$) compared to the total shipments ($n+14$). Based on the standard procedure for solving this equation, match each phase of the algebraic process with its corresponding mathematical expression.

A department manager uses the proportion $\frac{n}{n+14} = \frac{5}{7}$ to determine the number of full-time employees ($n$) relative to the total number of staff members ($n+14$) in a newly formed division. According to the algebraic solution for this proportion, the value of $n$ is ____.

In the process of solving the proportion $\frac{n}{n+14} = \frac{5}{7}$ for a staffing ratio, the equation is simplified to ${}7n = 5n + 70$. Subtracting ${}5n$ from both sides to isolate the variable terms results in the linear equation ${}2n = 70$.