The Perez family has 100 more shares of stock b than of stock A. The current price per share of stock A is 18.50 and of stock B is $24.75. At most how many shares of each do they have if the average price per share is greater than $22?

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The Perez family has 100 more shares of stock b than of stock A. The current price per share of stock A is 18.50 and of stock B is $24.75. At most how many shares of each do they have if the average price per share is greater than $22?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Any idea?
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This is what I got so far
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very good, go ahead, solve for x
x is greater than 366.6
so would my answers be a=366 and b=466?
ops I mean x is less than 366.6
\(\dfrac{18.50 x +24.75 (x+100)}{2x+100}\geq 22\) \(18.50x +24.75 x +2475 \geq 22(2x+100)\geq 44x +2200\) \(43.25x +2475 \geq 44x +2200\) \(0.75 x \leq 475\) \(x \leq 633.33\)
isnt -2475+2200= -275?
oh, yeah, my bad!! I am sorry
Anyways thanks for the help and clarification!

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