SOLUTION: a box contains 30 coins (5 cents, 10 cents, 25 cents and 50 cents)with a total value of Dollar 6.45. There are twice as many 10 cents coins as 25 cents coins and 2 more 50cents coi

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Question 931172: a box contains 30 coins (5 cents, 10 cents, 25 cents and 50 cents)with a total value of Dollar 6.45. There are twice as many 10 cents coins as 25 cents coins and 2 more 50cents coins than 5 cents coins. How many of each kind of coins are there?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
x+y+z+w=30
5x+10y+25z+50w=645
y=2z
w=x+2

Substitute 2z fo y and x+2 for w in the first two equations:

x+2z+z+x+2=30      5x+10(2z)+25z+50(x+2)=645

Simplify

2x+3z+2=30         5x+20z+25z+50x+100=645
  2x+3z=28                55x+45z+100=645
                              55x+45z=545
                               11x+9z=109

     

So we have the system:

  2x+3z=28
 11x+9z=109

Multiply the top equation by -3 and add the bottom equation:

 -6x-9z=-84
 11x+9z=109
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  5x   = 25
      x=5

You finish:

x = 5, y = 12, z = 6, w=7

Edwin