# SOLUTION: I have 7 bags of marbles. There are 200 marbles in total. Using the clues below, work out how many marbles are in each bag. Bag 1 + Bag 2 = 57 marbles Bag 2 + Bag 3 = 83 marble

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 Question 84858: I have 7 bags of marbles. There are 200 marbles in total. Using the clues below, work out how many marbles are in each bag. 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 Thank you so much for your help. I tried to figure this out but came to no avail.Found 2 solutions by jim_thompson5910, rapaljer:Answer by jim_thompson5910(28595)   (Show Source): You can put this solution on YOUR website!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 ``` a + b = 57 b + c = 83 c + d = 71 d + e = 43 e + f = 66 f + g = 43 ``` Also since we know how many marbles there are total, we can use this equation: ``` a+b+c+d+e+f+g=200 ``` 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") ``` a+b+c+d+e+f+g=200 -(a+b =57) -( c+d =71) -( f+g=43) ------------------- e =29 ``` So we know that bag 5 has 29 marbles Now plug in e=29 to find f ``` Bag 6: 29 + f = 66 f = 37 ``` So we know that bag 6 has 37 marbles Now plug in f=37 to find g ``` Bag 7: 37 + g = 43 g = 6 ``` So we know that bag 7 has 6 marbles Now plug in e=29 to find d ``` Bag 4: d + 29 = 43 d = 14 ``` So we know that bag 4 has 14 marbles Now plug in d=14 to find c ``` Bag 3: c + 14 = 71 c = 57 ``` So we know that bag 3 has 57 marbles Now plug in c=57 to find b ``` Bag 2: b + 57 = 83 b = 26 ``` So we know that bag 2 has 26 marbles Now plug in b=26 to find a ``` Bag 1: a + 26 = 57 a = 31 ``` 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 Answer by rapaljer(4667)   (Show Source): You can put this solution on YOUR website!What you have here is 7 equations and 7 unknowns, unless someone sees a faster way to do this!! Let the 7 variables be x1, x2, x3, x4, x5, x6, and x7 respectively. Now, here are the equations: x1+ x2+ x3+ x4+ x5+ x6+x7=200 x1+x2=57 x2+x3=83 x3+x4=71 x4+x5=43 x5+x6=66 x6+x7=43 If you have a graphing calculator, like a TI85, 86, 83+, or 84, you may have a program that will solve this system called [SIMLT] or perhaps [POLYSMLT]. If you don't have a calculator, then try getting everything in terms of x1. Do this by starting with x2 =57-x1 Then x3 = 83-x2 x3=83-(57-x1) x3=26+x1 Next, x4= 71-x3 x4=71-(26+x1) x4=45-x1 x5=43-x4 x5=43-(45-x1) x5=-2+x1 x6=66-x5 x6=66-(-2+x1) x6=68-x1 x7=43-x6 x7=43-(68-x1) x7=-25+x1 Now, x1+ x2+ x3+ x4+ x5+ x6+x7=200 x1+(57-x1)+(26+x1)+(45-x1)+(-2+x1)+(68-x1)+(-25+x1)=200 x1+169=200 x1=31 x2=26 x3=57 x4=14 x5=29 x6=37 x7=6 That should do it!!! R^2 at SCC