Once each day, darlene writes in her personal diary and records what is the sun is shining or not. when she looked back through her diary, she found that over a period of 600 days, the sun was shining 60% of the time. she kept recording for another 200 days and then found that the total number of sunny days drop to 50%. how many of the final 200 days for sunny days?

For the initial 600 days the sun was shining for a total of 360 days. This can be found by converting the percentage to a decimal by dividing its value by 100 and then multiplying that value by the initial total number of days shining. 

(60/100) x (600) = 360 days

She then observes the sun for an additional 200 days increasing the total amount of days from 600 to 800. As a result the percentage of sunny days drops from 60% to 50%. To help solve the problem you have to determine what 50% of the new total amount of days is. 

(50/100) x 800 = 400 days 

Lastly to determine how many of the days during the final 200 days were sunny subtract the number of sunny days from the first equation from the second. 

400 days - 360 days = 40 days 

This means that 40 of the final 200 days were sunny.