Chapter 6.1, Problem 38MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connections clearly and succinetly, and of uncovering pattern and structure.

Edges vs. vertices. Someone chalked a graph outside your dorm. You observe that the number of edges is twice the number of vertices. You also see that the number of edges times the number of vertices is equal to 30 plus four times the number of vertices. Let V be the number of vertices in the graph and E the number of edges. Write an equation showing the relationship between V and E and another equation involving EV. Use these two equat ions to find the value of V.