Homer is giving some cookies to each of his three brothers. To the oldest, he gives half of the cookies and half a cookie. He then gives half of what is now left and half a cookie to his second brother. Finally, he gives half of what is now left and half a cookie to his second brother. At no time is a cookie broken or cut. How many cookies did Homer have to begin with?
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great explanation. But may be explain the steps a little better.
Make it easier to understand
You are all asking for him to explain better like he did great y'all just looking for the answer online
To find out how many cookies Homer had to begin with, we can work backwards step by step.
Step 1: Giving half of the cookies and half a cookie to the oldest brother
Let's say the number of cookies Homer had to begin with is C.
Homer gives half of the cookies and half a cookie to his oldest brother, which means he retains the other half and half a cookie.
So after giving, Homer has (C/2) + 0.5 cookies left.
Step 2: Giving half of what is now left and half a cookie to the second brother
Homer then gives half of what is now left, which is (C/2) + 0.5, along with half a cookie to his second brother.
After this, Homer retains the other half and half a cookie.
So after giving, Homer has [(C/2) + 0.5]/2 + 0.5 cookies left.
Step 3: Giving half of what is now left and half a cookie to the third brother
Finally, Homer gives half of what is now left, which is [(C/2) + 0.5]/2 + 0.5, along with half a cookie to his third brother.
After this, Homer retains the other half and half a cookie.
So after giving, Homer has [[(C/2) + 0.5]/2 + 0.5]/2 + 0.5 cookies left.
Since at the end Homer has zero cookies left, we can set up an equation to solve for C:
[[[(C/2) + 0.5]/2 + 0.5]/2 + 0.5] = 0
Now we can solve the equation step by step by simplifying and isolating C.
Step 1: Remove the brackets:
[(C/2) + 0.5]/2 + 0.5 = 0
Step 2: Multiply both sides by 2 to eliminate the denominators:
[(C/2) + 0.5] + 1 = 0
Step 3: Simplify:
C/2 + 0.5 + 1 = 0
Step 4: Combine like terms:
C/2 + 1.5 = 0
Step 5: Subtract 1.5 from both sides:
C/2 = -1.5
Step 6: Multiply both sides by 2 to isolate C:
C = -3
However, since the number of cookies cannot be negative, it appears there might be an error or inconsistency in the problem statement. Please double-check the information provided.
If he had three brothers, the third got nothing, and the second brother got cookies twice!
Assuming he gave everything away, and working backwards:
"Finally, he gives half of what is now left and half a cookie to his second brother."
means at the end, he gave away the last one. (half of ONE that is left, and the other half).
"He then gives half of what is now left and half a cookie to his second brother."
So he had three to start, half of what is left is one and a half, plus half makes two. That leaves one.
"To the oldest, he gives half of the cookies and half a cookie."
After this, he had three, so half is three and a half, and he started with 7.
Conclusion: he started with 7 cookies.
In fact, if he had N brothers, he needs a minimum of 2N-1 cookies to start with.