Final answer:
To determine what percent of the total food expenses each camper paid, we evaluated if the provided statements were sufficient. Statement (1) and Statement (2) alone do not provide enough information, but used together, they allow us to solve for the unknowns and determine each camper's share. Therefore, both statements together are sufficient.
Step-by-step explanation:
To ascertain what percent of the total food expenses each camper paid, we need to determine if the provided statements are sufficient to calculate the individual share of the total cost. The total cost for food for all campers is expressed as x campers times y dollars, or xy dollars.
Statement (1) implies that if x - 1 campers each paid y + 1 dollars, the total cost would remain the same. Expressing this mathematically: (x - 1)(y + 1) = xy. Statement (1) alone is not sufficient as it provides only one equation with two unknowns.
Statement (2) indicates that if there were half as many campers, each camper would owe 7 dollars more. This can be expressed as 0.5x(y + 7) = xy. Statement (2) alone is not sufficient because it also represents a single equation with two unknowns.
Using both statements together, however, provides us two distinct equations, which can be solved simultaneously to determine the values of x and y, and hence the share of total expenses each camper paid. Therefore, the answer is (c), both statements together are sufficient.