SOLUTION: I have 7 bags of marbles. There are 200 marbles in total. bag 1 + bag 2 = 57 marbles bag 2 + bag 3 = 83 marbles bag 3 + bag 4 = 71 marbles bag 4 + bag 5 = 43 marbles bag 5

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Question 124754: I have 7 bags of marbles. There are 200 marbles in total.
bag 1 + bag 2 = 57 marbles
bag 2 + bag 3 = 83 marbles
bag 3 + bag 4 = 71 marbles
bag 4 + bag 5 = 43 marbles
bag 5 + bag 6 = 66 marbles
bag 6 + bag 7 = 43 marbles
How many marbles are in each bag?

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
I have 7 bags of marbles. There are 200 marbles in total.
:
Change the bag numbers to letters
bag a + bag b = 57 marbles
bag b + bag c = 83 marbles
bag c + bag d = 71 marbles
bag d + bag e = 43 marbles
bag e + bag f = 66 marbles
bag f + bag g = 43 marbles
How many marbles are in each bag?
:
Try to get everything in terms of a
b = -a + 57
:
c = -b + 83
c = -(-a+57) + 83; substitute for b
c = +a - 57 + 83
c = a + 26
:
d = -c + 71
d = -(a+26) + 71; substitute for c
d = -a - 26 + 71
d = -a + 45
:
e = -d + 43
e = -(-a+45) + 43; substitute d
e = +a - 45 + 43
e = a - 2
:
f = -e + 66
f = -(a-2) + 66; substitute for e
f = -a + 2 + 66
f = -a + 68
:
g = -f + 43
g = -(-a+68) + 43
g = +a - 68 + 43
g = a - 25
:
Substitute for b thru g in order = 200
a + (-a+57) + (a+26) + (-a+45) + (a-2) + (-a+68) + (a-25) = 200
:
4a - 3a + 57 + 26 + 45 - 2 + 68 - 25 = 200
:
a + 169 = 200
a = 200 - 169
a = 31 marbles in bag 1
:
Find the values b thru g by substituting for a:
b = -31 + 57 = 26 in bag 2
c = 31 + 26 = 57 in bag 3
d = -31 + 45 = 14 in bag 4
e = 31 - 2 = 29 in bag 5
f = -31 + 68 = 37 in bag 6
g = 31 - 25 = 6 in bag 7
:
Check our solutions using the above values:
31 + 26 + 57 + 14 + 29 + 37 + 6 = 200 total