Question

angelina and brad jointly buy the gourmet chocolate - strawberry cake shown in the figure to the right. the price of this fancy cake is $150. suppose that angelina values strawberry cake four times as much as she values chocolate cake. complete parts (a) through (c) below.
(c) find the dollar value to angelina of the strawberry sliver shown in figure to the right.
$
(round to the nearest cent as needed.)

Explanation:

Step1: Assign value variables

Let $x$ = value of 1° of chocolate cake. Then $4x$ = value of 1° of strawberry cake.

Step2: Calculate total cake degrees

Total degrees in a circle: $360^\circ$

Step3: Find strawberry/chocolate degrees

From the top figure: 3 strawberry slices, each $50^\circ$ (since $150^\circ$ total strawberry), so chocolate = $360 - 150 = 210^\circ$.

Step4: Set total value equation

Total cake value: $210x + 150(4x) = 150$
Simplify: $210x + 600x = 150$ → $810x = 150$
Solve for $x$: $x = \frac{150}{810} = \frac{5}{27}$

Step5: Value of 15° strawberry slice

Value = $15 \times 4x = 15 \times 4 \times \frac{5}{27}$
Calculate: $15 \times 4 = 60$; $60 \times \frac{5}{27} = \frac{300}{27} \approx 11.11$

Answer:

$\$11.11$