SOLUTION: A change maching contains nickels,dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the

Algebra ->  College  -> Linear Algebra -> SOLUTION: A change maching contains nickels,dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the       Log On


   

Question 158114: A change maching contains nickels,dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the number of coins of each type in the machine.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A change maching contains nickels,dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the number of coins of each type in the machine.

>>...There are 75 coins in the machine...<<

N+%2B+D+%2B+Q+=+75

>>...the value of the coins is $7.25...<<

.05N+%2B.10D+%2B+.25Q+=+7.25 

We remove the decimals by multiplying through
by 100:

5N%2B10D%2B25Q=725

We can also simplify it further by dividing
through by 5

N%2B2D%2B5Q=145


>>...There are 5 times as many nickels as dimes...<<

N=5D

So we have this system of equations:

system%28N%2BD%2BQ=75%2CN%2B2D%2B5Q=145%2CN=5D%29

Can you solve that system?  If not post again
asking how.

Solution:  

50 nickels, 10 dimes, 15 quarters

Edwin