```Question 84858
Lets use these variables for each bag:
Bag 1 = a
Bag 2 = b
Bag 3 = c
Bag 4 = d
Bag 5 = e
Bag 6 = f
Bag 7 = g

Now set up the following system of equations

<pre>

a + b = 57
b + c = 83
c + d = 71
d + e = 43
e + f = 66
f + g = 43

</pre>

Also since we know how many marbles there are total, we can use this equation:

<pre>

a+b+c+d+e+f+g=200

</pre>

Now subtract (a+b=57), (c+d=71), and (f+g=43) from a+b+c+d+e+f+g=200 to eliminate everything but one bag (in this case bag 5 which is denoted "e")

<pre>

a+b+c+d+e+f+g=200
-(a+b          =57)
-(    c+d      =71)
-(          f+g=43)
-------------------
e    =29

</pre>

So we know that bag 5 has 29 marbles

Now plug in e=29 to find f
<pre>

Bag 6:

29 + f = 66

f = 37

</pre>

So we know that bag 6 has 37 marbles

Now plug in f=37 to find g
<pre>

Bag 7:

37 + g = 43

g = 6

</pre>

So we know that bag 7 has 6 marbles

Now plug in e=29 to find d
<pre>

Bag 4:

d + 29 = 43

d = 14

</pre>

So we know that bag 4 has 14 marbles

Now plug in d=14 to find c
<pre>

Bag 3:

c + 14 = 71

c = 57

</pre>

So we know that bag 3 has 57 marbles

Now plug in c=57 to find b
<pre>

Bag 2:

b + 57 = 83

b = 26

</pre>

So we know that bag 2 has 26 marbles

Now plug in b=26 to find a
<pre>

Bag 1:

a + 26 = 57

a = 31

</pre>

So we know that bag 1 has 26 marbles

So here's a summary of all of the bags:

Bag 1 = 31 marbles
Bag 2 = 26 marbles
Bag 3 = 57 marbles
Bag 4 = 14 marbles
Bag 5 = 29 marbles
Bag 6 = 37 marbles
Bag 7 = 6 marbles

Check:

31+26+57+14+29+37+6=200
200=200 ```