Let the number of coffee cups sold = c
Let the number of the newspaper sold = n
Let the number of gums sold = g

Compared to cups of coffee, he sells twice as many packs of gum and three times as many newspapers
g = 2c and n = 3c

Price of c = $1.25
Price of n = $0.50
Price of g = $0.35

Total gross sales = (1.25 * c) + (0.50 * n) + (0.35 * g)
=1.25c + 0.50n + 0.35g where n = 3c and g = 2c
Therefore, total gross sales = 1.25c + (0.50 * 3c) + (0.35 * 2c)
=1.25c + 1.5c + 0.7c
=3.45c

Total sales for any given day = $3.45 * c; where c = quantity of cups of coffee which must be a positive integer

Target question => Which of the following could be the amount of his total gross sales on a given day?

For $345.00 =>
3.45c/3.45 = 345/3.45
c = 100, c is a positive integer so gross sales could be $345.00

For $58.65 =>
3.45c = 58.65 and c = 17
c is a positive integer, gross sales could be $58.65

For $22.15 =>
3.45c = 22.15 and c = 6.42
It is not possible to sell a fraction of a cup of coffee. c is positive but not an integer so gross sales cannot be $22.15

Only option I and II is possible
Answer = B