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David's New Year's Resolution is to work out at the gym every day. After each workout, he goes to the gym's bar and orders a one cup smoothie that is $\cfrac{1}{4}$ protein powder, $\cfrac{1}{3}$ almond milk, and equal parts strawberries and bananas.

The cost of the smoothie is equal to the sum of its components. Per full cup, protein powder costs $\$12$, almond milk costs $\$9$, and fruits cost $\$8$.

How much did one of David's smoothies cost?

A

$\$9.66$

B

$\$9.50$

C

$\$9.33$

D

$\$9.00$

E

$\$8.75$

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