Answer:
8 fifty cents coin.
Explanation:
Let's assign variable for the unknown number of coins.
Let there are 'x' number of $1 coins
'y' number of 20 cent coins
'z' number of 50 cent coints.
Totally there are 26 coins.
So, x+y+z=26
Now, there are 6 more $1 coins than 20-cent coins.
We can set up equation for this as
x= y+6
Now, total value of these coins is $17.20
We can setup equation as
100 x+20 y+50 z=1720
Now, substitute x as y+6
100(y+6) +20 y+50 z =1720
Distribute the 100 to get rid ( )
100 y+600 +20 y+50 z=1720
Combine like terms
120 y+50 z= 1120
Keep this equation as it is.
Plug in x as y+6 into x+y+z=26
y+6+y+z=26
2y+z=20
Now, take the two equations
2y+z=20
120y+50z=1120
Multiply first equation by -60 to eliminate the y terms when we add them.
-120y-60z=-1200
120y+50z= 1120
-------------------------
-10z =-80
Divide both sides by -10
z=8
Now, plug in z as 8 into 2y+z=20
2y+8 =20
Subtract both sides 8
2y=12
Divide both sides by 2
y=6
Now, plug in y, z values into the first equation.
x+6+8=26
x+14=26
Subtract both sides 14
x=12
So, there are eight 50-cent coins.