Solve this probiem using a system of equations; Colin has a jar of quarters and nickels, The jar has 15 coins atrogether, The total value of the coins is \( \$ 2.75 \). How many of each coin does Colin have?

To solve the problem, we start by letting \( q \) represent the number of quarters and \( n \) represent the number of nickels. We can set up a system of equations based on the information given. 1. The total number of coins equation: \[ q + n = 15 \] 2. The total value equation (in cents): \[ 25q + 5n = 275 \] Now, let's solve the system. From the first equation, we can express \( n \) in terms of \( q \): \[ n = 15 - q \] Next, we substitute this expression for \( n \) into the second equation: \[ 25q + 5(15 - q) = 275 \] Expanding and simplifying gives: \[ 25q + 75 - 5q = 275 \] \[ 20q + 75 = 275 \] \[ 20q = 200 \] \[ q = 10 \] Now, substitute \( q \) back into the equation for \( n \): \[ n = 15 - 10 = 5 \] Thus, Colin has 10 quarters and 5 nickels.