Shefali goes to a farmers' market every Saturday. Two Saturdays ago, Shefali purchased 3 apples and 4 oranges for a total of $3.47. Last Saturday, she purchased 12 oranges, but no apples, and spent $6.36. Today, she only has one $10 bill. Given that none of the prices have changed over the last 3 weeks, what is the maximum number of apples she can purchase today?

(Note: No sales tax is charged at this farmers' market.)

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We can write equations for the situations described to obtain the price of each apple, $A$.

The price of 12 oranges, $O$:

$$12O = 6.36$$ $$O = 0.53$$

3 apples and 4 oranges cost $3.47:

$$3A + 4O = 3.47$$ $$3A + 4(0.53) = 3.47$$ $$3A + 2.12 = 3.47$$ $$3A = 1.35$$ $$A = 0.45$$

With $10,

$$Ax = \$10$$ $$(0.45)x = \$10$$ $$x = 22.2 \approx \boxed{22}$$