Are needed to prepare for the fete. each can make either 2 large cakes or 35 small cakes per hour. the kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. how many are required?

You require 10 helpers

Step-by-step explanation:

The problem could be solved in many ways ( like using an optimization software) but I propose you this.

Start with production of large cakes.  In the time kitchen is available one helper could make, if only works in large cakes:

(2 large cakes / 1 hour) * (3 hours ) = 6 large cakes

So with 3 helpers using all their 3 hours we would have

3 helpers *6 large cakes /helper  = 18 large cakes.

We need 2 more large cakes so we can use one more helper and in his first hour he can produce

(2 large cakes / 1 hour) * (1 hour ) = 2 large cakes

The 4th helper has two hours of work left so he can produce small cakes.

(35 small cakes/hour* 2 hours = 70 small cakes.

With 4 helpers we have the 20 large cakes and 70 small ones. We still have to makes

700 - 70 = 630 small cakes left

In the 3 hour period a helper can make

(35 small cakes / 1 hour) * (3 hours ) = 105 large cakes

So if 1 helper does  105 large cakes  we would need to finish production with

630 / 105 =  6 helpers

So in total we have 3 helpers in only large cakes 6 in only small cakes and one helper doing both - total 10 helpers