Gracie, Mary, and Nancy each have a small collection of seashells. Gracie has 5 more than times the number of shells Mary has. Nancy has 1 more than times the number of shells Mary has. Gracie and Nancy have the same number of shells. If x is the number of shells Mary has, identify the equation that represents this situation and identify its solution.

First, let's name or variables. Let us name Gracie's number of seashells as G, Nancy's number of seashells as N and Mary's number of seashells is x. The first statement would give an algebraic expression of G = x + a5. The second statement gives N = x + b1. Also, G = N hence x + a5 = x + b1. Clearly, there are lacking values noted as a and b in the equation. Given a and b we can solve for x.