   SEARCH HOME Math Central Quandaries & Queries  Question from Rapin, a student: Dear Sir, Please help to solve this question; In 15 days, 4 white hens and 3 red hens lay eggs equal to 3 white hens and 5 red hens lay eggs in 12 days , how many days that white hens can lay eggs the same amount as red hens lay eggs in 20 days ? rdgs rapin We have two responses for you

Rapin,

Suppose that a white hen lays w eggs per day and a red hen lays r eggs per day. Thus in 20 days a red hen will lay 20 × r eggs. The question asks you to find the number of days d so that d × w = 20 × r.

How many eggs in total are laid by 4 white hens and 3 red hens in 15 days? What about 3 white hens and 5 red hens in 12 days?

Does this help?
Penny

Hi Rapin,

Let W = the number of eggs a white hen lays in a day and R = the number of eggs a red hen lays in a day.

Then 4W + 3R = the number of eggs laid by 4 white hens and 3 red hens in 15 days.

Also, 3W + 5R = the number of eggs 3 white hens and 5 red hens can lay in 12 days.

Since you've been told these two totals are the same, then
4W + 3R = 3W + 5R

Red hens can lay 20R eggs in twenty days. So you need to know what is 20R/W.

Can you solve the last equation for 20R/W?

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.