Given condition is : Each day of the month Carl earns an allowance in cents equal to the square of that date of the month.
This simplifies that if the date is 3rd Carl will earn 9 cents, if the date is 15th, he will earn 225 cents etc.
So, the maximum days in a month is 31. So the maximum he can earn in a day will be: [tex]31^{2}=961[/tex]
Hence, in a single day he can earn 961 cents.
