Chapter 3, Problem 14E

Marla and five other friends jointly buy the chocolate-strawberry-vanilla cake shown in Fig. 3-18(a) for $30 and plan to divide the cake fairly among themselves. After much discussion, the cake is divided into the six equal-sized slices $s_1,s,\mathrm{...},s_6$ shown in Fig. 3-18(b). Suppose that Marla values vanilla cake twice as much as chocolate cake and chocolate cake three times as much as strawberry cake.

a. Find the dollar value to Marla of each of the slices $s_1$ through $s_6$.

b. Which of the slices $s_1$ through $s_6$ are fair shares to Marla?