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

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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) About Me  (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) About Me  (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 

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
a%5Bn%5D=9%2B%28n-1%29%2A3

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

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
a%5Bn%5D=39%2B%28n-1%291

Set them equal:

9%2B%28n-1%293%22%22=%22%2239%2B%28n-1%291

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

Edwin

Answer by ikleyn(52787) About Me  (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.

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