Kate has some oranges with her. She eats half of her oranges every day. After eating the oranges, she is given four more oranges. After 3 days, she is left with 32 oranges. How many oranges she had in beginning?
Suppose Kate has T oranges in beginning.
She eats half of her oranges and then gets 4 more oranges daily.
If she has N oranges on a day, she will have [(N/2) + 4] at end of day.
Number of oranges after 1 day = (T/2) + 4 = 0.5T + 4
Number of oranges after 2 days = ((0.5T + 4)/2) + 4
= 0.25T + 6
Number of oranges after 3 days = ((0.25T + 6)/2 ) + 4
= 0.125T + 7
This should be equal to 32.
⇒ 0.125T + 7 = 32
⇒ T = 25/0.125 = 200
∴ Kate had 200 oranges in beginning.