Proportions and Ratios question. Help?

Question

This is the problem at hand: Farmer John has 41 hens. If he had one more solid colored hen, then exactly one-third of his hens would be speckled.
From years of experience, Farmer John knows that one-half of the speckled hens will lay speckled eggs and that each hen
and a half will lay an egg and a half in a day and a half. After how many full days will Farmer John have 11 dozen
speckled eggs to sell?
Explain your reasoning

I am able to do this problem when I add one more hen so Farmer John has 42 hens. However, he only has 41 and I am just not sure how to go about figuring out this problem. If he had 42 colored hens then exactly 1/3 of them are speckled. He only has 41 though?

Answer 1

Step 1. If Farmer John had 42 hens, then one third would be speckled.

One third of 42 is 14, so that would mean 14 speckled hens.

Step 2. He only has 41 hens.

So he must have 14 speckled hens and 27 solid-colored hens.

Step 3. Only half of the speckled hens lay speckled eggs.

Half of 14 is 7. So 7 hens lay speckled eggs.

Step 4. Each hen and a half lays an egg and a half in a day and a half.

That means 1 hen lays 1 egg in 1 and a half days.

So in 1 day, 1 hen lays two-thirds of an egg.

Step 5. Multiply that by 7 hens.

Each lays two-thirds of an egg per day.

So 7 hens lay 14-thirds eggs per day, which is about 4 point 67 eggs per day.

Step 6. Farmer John wants 11 dozen speckled eggs.

That is 132 eggs.

132 divided by 4 point 67 is about 28 point 29.

So the answer is 29 full days.

Answer 2

 

 

When the problem says "if he had one more solid ..." , this raises his total to 42 hens.

 

Do you need more help?

 

14 speckled, one half will lay speckled eggs , each hen and a half, will lay an egg and a half, in a day and a half    

 

this all has to be multiplied representing how many speckled eggs will be laid in a day and a half; then you have to find out how many days it takes to lay 11 dozen = 132

 

14 (1/2) (3/2) (3/2) (3/2) = ((189/8) will be laid in one and a half days

    

132 / (189/8) = 5.6 ; That is how many one and a half days it will take

 

5.6 (3/2) = 8.4

 

It will take 9 days to get 132 speckled eggs