In Part C, you determined that the proper ratio of packages of buns, packages of patties, and jars of pickles is 3:2:4. If you want to feed at least 540 people, but also maintain the proper ratio, what minimum number of packages of buns, packages of patties, and jars of pickles do you need, respectively?
Well, if we want to maintain the proper ratio of 3:2:4 while feeding at least 540 people, we should consider having a party for professional eaters or maybe start a burger revolution! 🍔
But I digress. Let's get back to the question. Since the ratio of packages of buns, packages of patties, and jars of pickles is 3:2:4, we can multiply each part of the ratio by an appropriate number to find the minimum number of packages of buns, packages of patties, and jars of pickles.
Multiply each part of the ratio by 4 to get: 3 x 4 = 12 packages of buns, 2 x 4 = 8 packages of patties, and 4 x 4 = 16 jars of pickles.
So, to feed at least 540 people while maintaining the proper ratio, you would need a minimum of 12 packages of buns, 8 packages of patties, and 16 jars of pickles. That should keep everyone happily munching away! 🎉
To determine the minimum number of packages of buns, packages of patties, and jars of pickles needed to feed at least 540 people while maintaining the proper ratio of 3:2:4, you can follow these steps:
Step 1: Calculate the total number of packages/jars needed to feed one group (3:2:4):
- Total packages/jars needed = 3 + 2 + 4 = 9
Step 2: Calculate the number of groups needed to feed at least 540 people:
- Number of groups = Number of people / Group size
- Group size = Total packages/jars needed = 9
- Number of people = 540
- Number of groups = 540 / 9 = 60
Step 3: Multiply the number of groups by the ratio to find the minimum number of packages/jars needed:
- Number of packages of buns = 3 x Number of groups = 3 x 60 = 180
- Number of packages of patties = 2 x Number of groups = 2 x 60 = 120
- Number of jars of pickles = 4 x Number of groups = 4 x 60 = 240
Therefore, to feed at least 540 people while maintaining the proper ratio of 3:2:4, you would need a minimum of 180 packages of buns, 120 packages of patties, and 240 jars of pickles, respectively.
To determine the minimum number of packages of buns, packages of patties, and jars of pickles needed to feed at least 540 people while maintaining the proper ratio of 3:2:4, we need to follow these steps:
Step 1: Calculate the scaling factor
The proper ratio is 3:2:4 (buns:patties:pickles). To find the scaling factor that will yield the minimum number of packages of each item, we need to calculate the least common multiple (LCM) of these numbers.
The LCM of 3, 2, and 4 is 12. Therefore, the scaling factor is 12.
Step 2: Multiply the ratio by the scaling factor
Multiply each number in the ratio (3:2:4) by the scaling factor (12) to get the minimum number of packages of buns, packages of patties, and jars of pickles needed, respectively:
Number of packages of buns = 3 x 12 = 36
Number of packages of patties = 2 x 12 = 24
Number of jars of pickles = 4 x 12 = 48
Therefore, to feed at least 540 people while maintaining the proper ratio, you will need a minimum of 36 packages of buns, 24 packages of patties, and 48 jars of pickles.
I need at least 540/4 = 135 pickles
half that many patties = 67.5 patties
3/4 * 135 = 101.25 of buns
now I could round the patty boxes up to 68 and the buns to 102 which is what I would do in practice
BUT
if I really need it to have integer packages I need to multiply by 4
135 * 4 = 540 pickles
67.5 * 4 = 270 patties
101.25*4 = 405 buns
very wasteful :)