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A chemist has come up with a new medicine called "Fixitall." Each batch of Fixitall costs him $\$0.40+0.5x$, where $x$ is the market price of the key ingredient. The chemist can sell each batch of Fixitall for anywhere from $\$5$ to $\$7$.

If the chemist wants to make a profit of at least $\$6$ from selling three batches, what is the minimum market price for the key ingredient that will allow him to do so?

A

$\$4.40$

B

$\$4.70$

C

$\$4.80$

D

$\$5.20$

E

$\$5.60$

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