Question

Talia bas 26 $1 coins, 20-cent coins, 50-cent coins. The number of $1 coins is 6 more than the number of 20-cent coins. The total value of the coins is $17.20. How many 50-cent coins are there?

Answer 1

Answer:

8 fifty cents coin.

Step-by-step 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.