lucy has 77 blank recipe cards. she divided her recipe box intpo 9 sections. if 5 sections have 1 more card than all the other sections, how many cards are in each section?
Well, if Lucy has 77 recipe cards and she divided them into 9 sections, we can start by dividing 77 by 9 to get roughly 8.5555555. But that doesn't really work because we can't have a fraction of a card, right? So let's try to distribute the cards in a way that accommodates the extra cards in 5 sections.
Let's start with each section having 8 cards, like we calculated earlier. That gives us a total of 72 cards. But if 5 sections have 1 more card, we need to account for those extra cards. So let's add 1 more card to each of those 5 sections. Now we have an extra 5 cards.
Since 72 + 5 = 77, we know that each of the 4 remaining sections will have 8 cards, while the 5 sections with extra cards will have 9 cards each.
So, in conclusion, 4 sections will have 8 cards each, while the remaining 5 sections will have 9 cards each.
To find the number of cards in each section, we can start by dividing the total number of cards by the number of sections. In this case, Lucy has 77 recipe cards divided into 9 sections.
77 / 9 = 8 remainder 5
Since 5 sections have 1 more card than the other sections, we need to distribute the remainder. Adding 1 to each of the 5 sections:
77 / 9 = 8
So, each section will have 8 cards, except for 5 of the sections which will have 8 + 1 = 9 cards.
To solve this problem, we need to determine the number of cards in each section.
Let's start by finding the total number of extra cards in the 5 sections. Since each of the 5 sections has 1 more card than the other sections, we can calculate the total number of extra cards as follows:
Total extra cards = 5 * 1 = 5 cards
Now, we can calculate the total number of cards in the 5 sections by adding the total extra cards to the number of cards in each of these sections:
Total cards in 5 sections = (Number of cards in each section) + (Total extra cards)
Total cards in 5 sections = (Number of cards in each section) + 5
We know that Lucy has a total of 77 blank recipe cards. Since there are 9 sections in total, the number of cards in each of the remaining 4 sections (which do not have any extra cards) can be calculated by subtracting the total number of cards in the 5 sections from the total number of cards:
Number of cards in each of the remaining 4 sections = (Total number of cards - Total cards in 5 sections)/Number of remaining sections
Number of cards in each of the remaining 4 sections = (77 - Total cards in 5 sections)/4
Now, let's calculate the number of cards in each section by dividing the total remaining cards equally among the remaining 4 sections:
Number of cards in each section = Number of cards in each of the remaining 4 sections / Number of remaining sections
Number of cards in each section = (77 - Total cards in 5 sections) / 4
Finally, we can substitute the value we found for the total cards in 5 sections in our previous equation to calculate the number of cards in each section:
Number of cards in each section = (77 - (Number of cards in each section + 5)) / 4
Now, we can solve this equation to find the value for the number of cards in each section.