There are 57 coins in a jar. Either quarters or nickels. The total is 11.05. How many of each coin are there ?

Question

there is a jar with 57 coins in it 

either quarters or nickels. 

The total amount is $11:05

how many of each coin are there ? I'm so confused. Help. 

Answer 1

 

1)   Q + N  =  57

   or  

 

1)   Q  =  57 - N

 

 

and

 

 

2)   $0.25 * Q  +  $0.05 * N   =   $11.05

 

or 

 

2)   25¢ * Q  +  5¢ * N  =  1,105¢

 

substitute equation 1 into equation 2 and solve for N

 

 

 25¢ * ( 57 - N ) + 5¢ * N = 1,105¢

 

 1425¢  -   25¢ * N   +  5¢ * N   =  1105¢ 

or

1425¢ - ( 20¢ * N ) = 1105¢

 

subtract  1105¢  from both sides, and add 20 1425¢ - 25¢ * N + 5¢ * N = 1105¢ * N to both sides

 

320¢   =   20¢ * N

 

divide both sides by 20¢, and you get

 

16  =  N

 

There are 16 nickels in the jar, and 57 - 16 ( = 41 ) quarters in the jar.

 

That's 80¢ in nickels and $10.25 in quarters, totaling $11.05