Question

At a party there is one bottle of coke for every 3 guests, one bottle of sprite for every 6 guests, and one bottle of lift for every 4 guests. There are 54 bottles of drink at the party. How many guests are there? At a party there is one bottle of coke for every 3 guests , one bottle of sprite for every 6 guests , and one bottle of lift for every 4 guests . There are 54 bottles of drink at the party . How many guests are there ?​

Answer 1

72 guests

Explanation:

We can add up the numbers of bottles per guest, then use that total to find the number of guests from the number of bottles.

Setup

Let g represent the number of guests at the party. Then there are ...

• g/3 bottles of coke
• g/6 bottles of sprite
• g/4 bottles of lift

The total number of bottles is ...

g(1/3 +1/6 +1/4) = 54

Solution

Multiplying by the inverse of the coefficient of g, we find its value to be ...

g(4/12 +2/12 +3/12) = g(9/12) = 54

g = 54(12/9) = 72

There are 72 guests at the party.