At a large picnic, there were 45 dishes served altogether. every 3 people shared a dish of cole slaw between them. every 4 people shared a dish of potato salad between them. every 6 people shared a dish of hot dogs between them. how many people were at the picnic?

There were 12·5=60 people at the picnic.

Step-by-step explanation:

If every 3 people shared a dish of Cole slaw between them, every 4 people shared a dish of potato salad between them and every 6 people shared a dish of hot dogs between them, then you can find the minimal number of people that can do such thing. Mathematically this is the least common multiplier LCM.

Since

then LCM(3,4,6)=2·2·3=12.

Suppose at the picnic were 12 people. If every 3 people shared a dish of Cole slaw between them, then 12 : 3 = 4 such dishes were served. If every 4 people shared a dish of potato salad between them, then 12 : 4 = 3 such dishes were served. If every 6 people shared a dish of hot dogs between them, then 12 : 6 = 2 such dishes were served. In total, 4 + 3 + 2 =9 dishes.

You know there were 45 dishes served altogether. 45 is 5 times more than 9, then the number of people at the picnic is 5 times  more than 12. Therefore, there were 12·5=60 people at the picnic.

its a i did it myself

step-by-step explanation: