Answer:
A = 10w
Explanation:
In the area formula, the coefficient of width is length. Here, that is ...
... A = 7w
7 is the coefficient of the width. Increasing it by 3 makes it be 10, so we have ...
... A' = 10w
_____
Comment on the problem statement
The problem does not make it clear whether area stays the same as the coefficient increases. We have assumed that it does not.
Also, the coefficient of width in the area formula has units of inches. "Increases by 3" makes no sense in this context. It would make sense for it to increase by 3 inches. The result is very different if the increase is 3 microns, for example.