1 egg, 1 potato, 2 apples and 2 cabbages are needed to initially make a salad for one person. When making the salad for additional people, half of the ingredients necessary for the first person are required for each subsequent person. If 6 cabbages are needed to make the salad for a certain group of people, how many eggs are needed?
if it is getting halved everytime, wotn the number of eggs needed go into decimals?
Hi @skandaextra1, The number of eggs will definitely go in decimals, but not as you are thinking of halving it every time you make a salad.
The answer for this goes like:
Cabbages requried to make salad for first person = 2
Cabbages requried to make salad for every subsequent person = (Cabbages requried to make salad for first person)/2 = 2/2 = 1
Eggs requried to make salad for first person = 1
Eggs requried to make salad for every subsequent person = (Eggs requried to make salad for first person)/2 = 1/2 = 0.5 (basically half an egg)
STEP 1: Make salad untill you use up 6 cabbage and count the number of times you made the salad
Salad 1 : 2 cabbages
Salad 2 : 1 Cabbage + 2 Cabbages from Salad 1 = 3 Cabbages
Salad 3 : 1 Cabbage + 3 Cabbages from Salad 1 = 4 Cabbages
Salad 4 : 1 Cabbage + 4 Cabbages from Salad 1 = 5 Cabbages
Salad 5 : 1 Cabbage + 5 Cabbages from Salad 1 = 6 Cabbages
STOP HERE
NOTE THAT SALAD WAS PREPARED 5 TIMES
So similarly, prepare salad for 5 times for calculating eggs
Salad 1 : 1 Egg
Salad 2 : 0.5 Egg + 1 Egg from Salad 1 = 1.5 Eggs
Salad 3 : 0.5 Egg + 1.5 Eggs from Salad 1 = 2 Eggs
Salad 4 : 0.5 Egg + 2 Eggs from Salad 1 = 2.5 Eggs
Salad 5 : 0.5 Egg + 2.5 Eggs from Salad 1 = 3 Eggs
I hope this solves your query
I would like to add an alternative approach using ratios.
We need to find out the total number of eggs used for the remaining guests. We know that 6 cabbages, in total, had been used. Of this, 2 have been used on the first guest, leaving 4 to be used for the remaining guests.
The ratios provided- 1:1:2:2- will be halved, since the recipe calls for only half of the ingredients, so my new ratio will be 0.5:0.5:1:1. I know that I have used 4 cabbages for the remaining guests, so I can use this information and the new ratios to get the actual number of items used (since ratios show me the simplified values). So, the total comes out to be 12. We need to find eggs, which are a 1/6th of the total (0.5/3). Therefore, number of eggs used on the subsequent guests are 2. Adding the one egg used for the initial guest, you will get the anser as 3. Hope this made snense.