Final answer:
To find the auditorium's capacity with a ratio of occupied to empty seats as 5:2 and 120 empty seats, we divide 120 by 2 to find the value of one part and multiply by the total parts (5+2) to get 420 seats as the total capacity.
Step-by-step explanation:
The question asks us to find the capacity of an auditorium where the ratio of occupied to empty seats is 5:2, and there are 120 empty seats. To solve this, we can use the concept of ratios. Since there are 2 parts of the ratio that correspond to 120 empty seats, each part is equivalent to 60 seats (120 empty seats ÷ 2 parts of the ratio). Because there are 5 parts occupied for every 2 parts empty, we multiply 60 seats (the value of one part) by 7 (the total parts of the ratio, which is 5 + 2) to find the total capacity of the auditorium.
The calculation is as follows:
- Value of one part: 120 empty seats ÷ 2 = 60 seats per part
- Total capacity: 60 seats × 7 parts = 420 seats
Therefore, the correct answer is 420 seats, which is option (c).