Harry went to collect eggs from four chicken coops. At the first coop he collected the eggs and put them in the basket.at the next coop,he doubled what he had.At the third coop, he collected 6 more but dropped and broke two on his way to the fourth coop. At the fourth coop, he added 4 more eggs. On his way home, he gave half of the eggs to his grandma and took the remaining nine eggs home to his mother. Explain how you solved this problem. How many eggs did Harry collect at the first coop?
X = the number of eggs collected at the first coop.
Then, after Coop 1 = X
......after coop 2 = 2X
......after coop 3 2X + 4
......after coop 4 2X + 8
Gave half to grandma leaving X + 4
Gave the remaining 9 to his mother
Making X + 4 = 9 or X = 5.
To solve this problem, we need to carefully go through the given information step by step.
1. At the first coop, Harry collected some eggs and put them in the basket. Let's call this number of eggs x.
2. At the second coop, Harry doubled the eggs he had. Therefore, he collected 2 times the number of eggs he had at the first coop, which is 2x.
3. At the third coop, Harry collected 6 more eggs. So now, he had 2x + 6 eggs.
4. Unfortunately, on his way to the fourth coop, Harry dropped and broke two eggs. This means he now had 2x + 6 - 2 = 2x + 4 eggs.
5. Finally, at the fourth coop, Harry added 4 more eggs. Therefore, the total number of eggs he had is 2x + 4 + 4 = 2x + 8 eggs.
6. On his way home, Harry gave half of the eggs to his grandma. That means he kept half of the eggs for himself. So, the number of eggs Harry took home is 1/2 * (2x + 8) = x + 4 eggs.
7. According to the problem, he took nine eggs home to his mother. Therefore, we can set up the equation x + 4 = 9 and solve for x.
x + 4 = 9
x = 9 - 4
x = 5
Hence, Harry collected 5 eggs at the first coop.