SOLUTION: Bridget's classroom started out with a collection of only 6 books, but she plans to purchase an additional 3 books per week. Cole's library started out with 38 books, and he will p

Algebra.Com
Question 1107560: Bridget's classroom started out with a collection of only 6 books, but she plans to purchase an additional 3 books per week. Cole's library started out with 38 books, and he will purchase another 1 book per week. At what week and amount of books will the two libraries be the same?
Found 3 solutions by mananth, mccravyedwin, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Bridget�s classroom started out with a collection of only 6 books, but she plans to purchase an additional 3 books per week. Cole�s library started out with 38 books, and he will purchase another 1 book per week. At what week and amount of books will the two libraries be the same?
Let number of weeks be denoted x
Bridget�s classroom started out with a collection of only 6 books, but she plans to purchase an additional 3 books per week
n1= number of books
n1=6+3x
Cole�s library started out with 38 books, and he will purchase another 1 book per week
n2= 38+1x

When will n1 be equal to n2
6+3x = 38+x
3x-x = 38-6
2x = 32
x = 16
amount of books in the two libraries will be sam be the same at 16 weeks







Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!
If you are studying arithmetic sequences (progressions), this is the way
you should do it.

Bridget's is an arithmetic sequence (progression) with a1=6+3=9 and d=3.
So her number of books on the nth week is 




Cole's is an arithmetic sequence with a1=38+1=39 and d=1.
So his number of books on the nth week is




Set them equal:



Simplify and solve for n.  You'll get 16 weeks.

Edwin
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

Solve it MENTALLY, without using equations. 

    Initial difference is 38-6 = 32 books.


    Each week the difference diminishes by 3-1 = 2 books.


    So, the difference becomes 0 (zero) in 32/2 = 16 weeks.

At this point, the MENTAL solution is just complete.

----------------

I placed this mental solution here in order for you better understand how simple the problem is.




RELATED QUESTIONS

Jasmine got a collection of books from her parents,35, and a collection of books from her (answered by josgarithmetic)
Jasmine got a collection of books from her parents, 35, and a collection of books from... (answered by richwmiller)
you are transferring to a new house. You have a collection of books but you can not take... (answered by Edwin McCravy)
I know the answer, which is 97, because I found it in the back of the book, but I can't... (answered by edjones,rajagopalan)
Darah wants to print a book she has written, and then sell it to the public. She has... (answered by ankor@dixie-net.com)
There are a certain amount of books. If we give these books only to the girls in the... (answered by josmiceli)
The school wants to have all of the students enrolled in social studies classes read the (answered by MathLover1)
-this is the whole question {{{highlight(cross(sori))}}} SORRY Sydney... (answered by ikleyn)
Finding number of books. Verna decided to sell her collection of paperback books. To... (answered by stanbon)