Final answer:
To consume 400 hotdogs, with every fourth person eating 3 hotdogs, it would take 534 people. This result is obtained by setting up a proportional ratio and solving for the number of people required.
Step-by-step explanation:
The question is centered on a straightforward proportional relationship in mathematics. If every fourth person consumes 3 hotdogs, we want to calculate how many people it takes to consume 400 hotdogs.
To do this, we can set up a ratio where 4 people eat 3 hotdogs, so we want to find how many groups of 4 it takes to reach 400 hotdogs.
Setting up a proportion, we have:
4 people : 3 hotdogs = x people : 400 hotdogs
This simplifies to:
3 hotdogs/4 people = 400 hotdogs/x people
We can solve for 'x' by cross-multiplication:
3x = 4 * 400
x = (4 * 400) / 3
x = 1600 / 3
x = 533.33
Since we can't have a fraction of a person, we round up, because we need full groups of 4 people to consume the hotdogs which gives us:
x = 534
Therefore, it will take 534 people for 400 hotdogs to be eaten, assuming every fourth person eats three hotdogs.