Three tired and hungry men went to sleep with a bag of apples. One man woke up, ate 1/4 of the apples, then went back to sleep. Later a second man woke up and ate 2/3 of the remaining apples, then went back to sleep. Finally, the third man woke up and ate 3/4 of the remaining apples. When he was finished there were 9 apples left. How many apples were in the bag originally? Please show working. Thanks
man1 ate 1/4, leaving 3/4
man2 ate 2/3 of 3/4 = 1/2, leaving 1/4
man3 ate 3/4 of 1/4 = 3/16, leaving 1/16
1/16 of total is 9, so the total is 144
check:
man1 ate 36, leaving 108
man2 ate 72, leaving 36
man3 ate 27, leaving 9
thank you mr.steve
To find out how many apples were originally in the bag, we need to work backwards from the information given.
Let's assume that the number of apples originally in the bag is "x".
According to the problem, the first man ate 1/4 of the apples, so the remaining apples would be 3/4 of x, which is (3/4)x.
The second man then ate 2/3 of the remaining apples, which means he ate (2/3) * (3/4)x = (2/4)x = (1/2)x apples. This leaves (1/2)x apples remaining.
Finally, the third man eats 3/4 of the remaining apples, which means he ate (3/4) * (1/2)x = (3/8)x apples. This leaves (1 - 3/8) = (5/8)x apples.
Given that there were 9 apples left after the third man ate, we can set up the following equation:
(5/8)x = 9
To solve for x, we can multiply both sides of the equation by (8/5):
x = 9 * (8/5)
x = 14.4
Since we cannot have a fraction of an apple, the original number of apples must be a whole number. Therefore, we can conclude that there were 14 apples originally in the bag.