How many rolls of each coin does he have?

Question

There are 50 dimes in a roll of dimes, 40 nickels in a roll of nickels, and 40 quarters in a roll of quarters. Rob has 12 rolls of coins with a total value of $70.00. He has 3 more rolls of nickels than dimes. How many rolls of each coin does he have?

Answer 1

Hey Ryan -- $2N, $5D, $10Q ... N+D paks => must be a multiple of $10 ... try 4N:1D ...

 

$13, $20 ==> 5N:2D:5Q ... Best regards, sir :)

Answer 2

d is number of rolls of dimes

n is number of rolls of nickels

q is number of rolls of nickels

 

d+n+q=12 (total number of rolls)

n=d+3 (3 more rolls of nickels than rolls of dimes)

50*.1*d+40*.05*n+40*.25*q=70 (sum of coins in roll, value of each coin, number of rolls equals total vale)

 

want to to take it from there?  Solve the three equations simultaneously, you'll get the number of rolls for each type of coin!

 

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d+n+q = 12

n=d+3

5d+2n+10q=70

 

5d+2(d+3)+10q=70

5d+2d+6+10q=70

7d+10q+6=70

7d+10q=64

 

d+d+3+q=12

2d+q+3=12

2d+q=9

20d+10q=90

 

20d+10q=90

-7d-10q=-64

13d=26

d=2  (numbr of dime rolls, value $10)

 

n=d+3=5 (number of nickel rolls, value $10)

2+5+q=12

q= 5 (number of quarter rolls, value $50)

 

check total value is $70 ... correct

check total number of rolls is 12 ... correct