When 6-year old Melanie arrived home from school, she was the first to eat cookies from a freshly baked batch. When 8-year old Felipe arrived home, he ate twice as many cookies as Melanie had eaten. When 9-year old Hillary arrived home, she ate 3 fewer cookies than Felipe. When 12-year old Nicholas arrived, he ate 3 times as many cookies as Hillary. Nicholas left 2 cookies, one for each of his parents. If Nicholas had eaten only 5 cookies, there would have been 3 cookies for each of his parents. How many cookies were in the original batch?
martinez
I'm sorry, I'm not sure what you are asking for. Could you please provide more context or clarify your question?
5
I apologize, but I'm not sure what you mean by "5". Could you please provide more context or clarify your question?
Let's solve this problem step by step.
First, let's calculate how many cookies Nicholas ate. We know that he ate three times as many cookies as Hillary and left 2 cookies for his parents. If he had eaten 5 cookies, there would have been 3 cookies for each of his parents.
Let's set up an equation to represent this information:
3(Hillary's cookies) + 2 = (Nicholas's cookies)
Plugging in the information where Nicholas ate only 5 cookies:
3(Hillary's cookies) + 2 = 5
Now let's solve this equation to find out how many cookies Nicholas originally ate:
3(Hillary's cookies) = 5 - 2
3(Hillary's cookies) = 3
Hillary's cookies = 1
So, Nicholas originally ate 3 times as many cookies as Hillary, which means he ate 3 * 1 = 3 cookies.
Now let's find out how many cookies Felipe originally ate. We know that he ate twice as many cookies as Melanie, so Felipe ate 2 * Melanie's cookies.
Since Hillary ate 1 cookie, we can say that Melanie ate 1/2 cookie because Felipe ate twice as many cookies.
Now let's find out how many cookies Melanie originally ate:
Melanie's cookies = 1/2
Therefore, Felipe originally ate 2 * 1/2 = 1 cookie.
Lastly, let's find out how many cookies were in the original batch. We know that Melanie ate 1/2 cookie, Felipe ate 1 cookie, Hillary ate 1 cookie, and Nicholas ate 3 cookies, totaling:
Melanie's cookies + Felipe's cookies + Hillary's cookies + Nicholas's cookies = 1/2 + 1 + 1 + 3
This simplifies to:
6 + 1/2
Therefore, there were 6 1/2 cookies in the original batch.