Answer:
We know that Trinity has a total of 20 quarters and nickels, so:
x + y = 20
We also know that the value of x quarters is 25x cents, and the value of y nickels is 5y cents. The total value of the coins is $2.00, which is 200 cents:
25x + 5y = 200
We now have two equations with two variables. We can solve for one variable in terms of the other in one of the equations and substitute that expression into the other equation.
Let's solve for y in terms of x in the first equation:
y = 20 - x
Substitute this expression for y into the second equation:
25x + 5(20 - x) = 200
Simplify and solve for x:
25x + 100 - 5x = 200
20x + 100 = 200
20x = 100
x = 5
Now that we know x = 5, we can use the first equation to find y:
x + y = 20
5 + y = 20
y = 15
Therefore, Trinity has 5 quarters and 15 nickels.
Explanation: