There are 30 coins all dimes and quarters on the table worth $5.10. How many quarters are there?

A)15 quarters
B)16 quarters
C)13 quarters
D)14 quarters

We can set up a system of equations.

x + y = 111

0.25x + 0.10y = 18.30

x + y = 111

Subtract 'y' to both sides:

x = -y + 111

Plug in '-y + 111' for 'x' in the 2nd equation:

0.25(-y + 111) + 0.10y = 18.30

Distribute 0.25 into the parenthesis:

-0.25y + 27.75 + 0.10y = 18.30

Combine like terms:

-0.15y + 27.75 = 18.30

Subtract 27.75 to both sides:

-0.15y = -9.45

Divide -0.15 to both sides:

y = 63

Plug this back into any of the two equations to find the 'x' value.

x + y = 111

x + 63 = 111

Subtract 63 to both sides:

x = 48

So there are 48 quarters and 63 dimes.

Step-by-step explanation:

Hope This Helps!

1/4 because there is 4 grades.