At the town picnic, 480 hot dogs and 320 hamburgers are barbequed. Find the maximum number of families that can attend if the hot dogs and hamburgers are divided equally for each family.(1 point)
Responses
160 families
40 families
80 families
120 families
To find the maximum number of families that can attend, we need to determine the least common multiple (LCM) of 480 and 320, and divide it by the number of hot dogs and hamburgers.
First, let's find the LCM of 480 and 320:
- Prime factorize 480: 480 = 2^5 * 3 * 5
- Prime factorize 320: 320 = 2^6 * 5
The LCM is the highest power of each prime factor: LCM(480, 320) = 2^6 * 3 * 5 = 1920
Now, we divide the LCM by the number of hot dogs and hamburgers to find the maximum number of families that can attend:
1920 / (480 + 320) = 1920 / 800 = 2.4
Since the number of families attending must be a whole number, we round down to the nearest whole number: 2.4 ≈ 2
Therefore, the maximum number of families that can attend is 2.
However, since the given answer choices do not include 2 as an option, there seems to be an error in the question or the answer choices provided.