Solve the problem using matrices.
-John has a jarful of quarters and nickels. There are 109 coins in the jar. The value of the coins is $15.25. How many of each type of coin are there?
A) 49 quarters; 60 nickels
B) 104 quarters; 5 nickels
C) 54 quarters ; 55 nickels
D) 60 quarters; 49 nickels

Question

Quizplus · Accepted Answer

Let $q$ represent the number of quarters and $n$ represent the number of nickels. We have two equations: $q + n = 109$ and $0.25q + 0.05n = 15.25$. Converting the second equation to cents for simplicity, we get $25q + 5n = 1525$. Solving this system of equations using matrices or substitution/elimination methods yields $q = 49$ and $n = 60$.

Solve the Problem Using Matrices