Three squirrels, Steve, Keith and Benjamin, have spent all day collecting nuts. At the end of the day they are very tired and go to bed. During the night, Steve wakes up and eats a nut. He then decides to take half of the remaining pile and hides it before going back to sleep. Keith then wakes up. He too is hungry, so he eats a nut. He also takes half of the remaining pile and hides it before going back to sleep. Finally, Benjamin wakes up, eats a nut and hides half of the remaining pile. In the morning, all of the squirrels share the remaining nuts equally between them and each goes off with four more nuts. Each squirrel then eats all the nuts he now us. How many nuts has Steve eaten in total?
81
28
Let's work backwards to find the original total number of nuts. Each squirrel went off with four more nuts, so before they did so, there were 12 more nuts in total. Therefore, after they shared the remaining nuts equally, there were 40 nuts in total.
Before Benjamin took half of the remaining pile, there were 80 nuts (double 40). Before Keith took half of the remaining pile, there were 160 nuts (double 80). And before Steve took half of the remaining pile, there were 320 nuts (double 160).
So, Steve ate one nut at night and hid half of the remaining 319, which is 159.5. Since he cannot give half a nut to anyone, we can assume that he rounded down and hid 159 nuts.
Therefore, Steve ate a total of 1 + (320-159)/2 = 81 nuts.
Correct! Steve ate a total of 81 nuts.
To calculate how many nuts Steve has eaten in total, we need to work through the steps of the problem.
Let's start by working backwards. We know that each squirrel ended up with four more nuts after sharing the remaining pile equally. This means that before sharing, each squirrel had four fewer nuts than what they ended up with. So, to find the number of nuts Steve, Keith, and Benjamin each had before sharing, we subtract 4 from how many nuts each squirrel had after sharing.
Since each squirrel eats all the nuts they have, this implies that the number of nuts each squirrel had before sharing is equal to the total number of nuts they ate. Therefore, to find how many nuts Steve ate in total, we need to calculate how many nuts he had before sharing and then subtract the number of nuts he had after sharing from that.
Let's go through the steps:
1. In the morning, each squirrel had four more nuts than what they had before sharing.
2. Since Steve had four more nuts in the morning, it means he had four fewer nuts before sharing.
3. Keith and Benjamin also had four fewer nuts before sharing.
Now, let's calculate how many nuts each squirrel had before sharing:
1. In the morning, each squirrel had four more nuts, so Steve had 4 + 4 = 8 nuts.
2. Keith and Benjamin also had four more nuts, so they each had 8 nuts too.
Next, let's calculate how many nuts each squirrel had after sharing:
1. Steve took half of the remaining pile and hid it, which means he had half of his original pile left. Since he had 8 nuts before sharing, he hid 8/2 = 4 nuts.
2. Keith also took half of the remaining pile, which means he also had half of his original pile left. Since he had 8 nuts before sharing, he hid 8/2 = 4 nuts.
3. Benjamin did the same, taking half of the remaining pile and hiding it. Since he had 8 nuts before sharing, he hid 8/2 = 4 nuts.
Now let's calculate how many nuts each squirrel had after sharing:
1. Steve had 8 nuts before sharing and hid 4, so he had 8 - 4 = 4 nuts after sharing.
2. Keith and Benjamin also had 8 nuts before sharing and hid 4, so they each had 8 - 4 = 4 nuts after sharing.
Finally, let's calculate how many nuts Steve ate in total:
1. Steve ate all the nuts he had after sharing, which is 4 nuts.
Therefore, Steve has eaten a total of 4 nuts.
Just start doing the math.
total nuts = x
Steve eats 1, leaving x-1, saves (x-1)/2
That leaves (x-1)/2 nuts
Now do the next step, and the next till you get down to a known amount.