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.