41. At a cafeteria, \( 25 \% \) of the sandwiches sold had chicken, \( 40 \% \) had fish and the remaining 70 sandwiches had ham. (a) What PERCENTAGE of the sandwiches had HAM? Answer. \( \qquad \) (1) (b) How many sandwiches were sold by the cafeteria? Answer. \( \qquad \) (c) How many MORE fish sandwiches than chicken sandwiches were sold by the cafeteria? Answer. \( \qquad \) (2)

To determine the percentage of sandwiches that had ham, we first note that if 25% had chicken and 40% had fish, this accounts for 65% of the total sandwiches sold. Therefore, the remaining sandwiches that had ham would be 100% - 65% = 35%. Consequently, 35% of the sandwiches had ham. Now, regarding the total sandwiches sold at the cafeteria, let’s denote the total number of sandwiches as \( x \). Since 35% of \( x \) is given to be 70 sandwiches, we set up the equation: \[ 0.35x = 70 \] Solving for \( x \), we get \( x = \frac{70}{0.35} = 200 \). Thus, 200 sandwiches were sold by the cafeteria. Lastly, let’s analyze the difference between fish and chicken sandwiches sold. If 25% of the sandwiches (200) had chicken, then: \[ \text{Chicken sandwiches} = 0.25 \times 200 = 50 \] And if 40% had fish, then: \[ \text{Fish sandwiches} = 0.40 \times 200 = 80 \] Therefore, the difference in quantity between fish and chicken sandwiches sold is: \[ 80 - 50 = 30 \] So, there were 30 more fish sandwiches than chicken sandwiches sold at the cafeteria. To summarize: (a) The percentage of sandwiches that had ham: \( 35 \% \) (b) The total number of sandwiches sold by the cafeteria: \( 200 \) (c) The number of more fish sandwiches than chicken sandwiches sold: \( 30 \)