Chapter 3, Problem 13E

Karla and five other friends jointly buy the chocolate-strawberry-vanilla cake shown in $\underset{\_}{\text{Fig}\text{. }3-18\left(\text{a}\right)}$ 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 $\underset{\_}{\text{Fig}\text{. }3-18\left(\text{b}\right)}$. Suppose that Karla values strawberry cake twice as much as vanilla cake and chocolate cake three times as much as vanilla cake.

$Figure3-18$

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

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