SOLUTION: John has 55 coins consisting of dimes, nickels and quarters. If the numbers of quarters are five more than twice the number of dimes, and the total value is 8.25. Find how many o

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Question 674717: John has 55 coins consisting of dimes, nickels and quarters. If the numbers of quarters are five more than twice the number of dimes, and the total value is 8.25. Find how many of each denomination of coin does he have?
I know that the answer is 20 nickels, 10 dimes, and 25 quarters. I have set up the chart and got x + y + z = 55 and then, 5y + 10y + 25z = 82500 and then I got stuck on the number of quarters are five times than twice the number of dimes. I wrote it as 25(y + 5) and this does not fit into an equation that I can work off of. I am confused. Please show me how to set it up. Thank you.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

John has 55 coins consisting of highlight%28x%29dimes, highlight%28y%29nickels and highlight%28z%29quarters.  

numbers of quarters are five more than twice the number of dimes

z+=+2x%2B5   

x + y + z = 55   Yes, good work  

y+=+55-x-z  0r   y = 55-x-%282x%2B5%29+=+55-3x-5 = (50-3x)

and the total value is 8.25. 

5y + 10x + 25z = 825   ||Careful, Cents does makes sense..however,  $8.25 is 825¢

Substituting

5(50-3x) + 10x + 25(2x+5) = 825

 250 - 15x + 10x + 50x + 125 = 825

            45x = 825-125-250

            45x = 450

              x = 10, number of dimes.   20 nickels and 25 quarters

and

 5%2A20+%2B+10%2A10+%2B+25%2A25+=+100+%2B+100+%2B+625+=+825