1 large pizza to 2 wrkers,1 chips to 3 workers, 1 drink to 4 workers. 26 items delivered. how many workers? how many items delivered

Question

around major holidays, many dorm workers have to work overtime, so bully planned a late night snack for the dorm workers.  He ordered 1 extra-large pizza for every 2 workers.  He ordered 1 large bag of potato chips for every 3 workers, and 1 two-liter bottle of cola for every four workers.  When the order arrived, 26 items were delivered.  How many dorm workers were working that evening?  How many of each item were delivered?

*I need to know how to set up this problem and why.  I know that these are ratios and I should probably set it up as # of workers over 2 workers/pizza etc.  I am just not sure how to work it out.  thanks

Answer 1

Solution

24 workers.



Suppose there are x workers. The number of pizzas delivered will be (x workers)/( 2 workers/pizza) and similarly for the other two items. The total number of items is then x/2 + x/3 + x/4 = 26. Solving for x, we find that there must be 24 workers that evening. We could also reason that the number of workers must be a common multiple of 2, 3, and 4. These multiples are 12, 24, 36, 48, 60, 72 . . . . Set up a ratio table, giving the number of items for each possible number of workers, to find that 24 workers result in the given numbers of items.