Question

26 nickels, dimes & quarters made $2.25. How many dimes were there if there were 10 times as many nickels as quarters?

Answer 1

To solve this problem, set up a system of equations using the given information. Then, solve the equations to find the values of the variables.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.

Let's denote the number of nickels as N, the number of dimes as D, and the number of quarters as Q.

We are given two pieces of information:

1. The total value of the coins is $2.25, so we can write the equation: 0.05N + 0.10D + 0.25Q = 2.25
2. There are 10 times as many nickels as quarters, so we can write the equation: N = 10Q

We can substitute the value of N from the second equation into the first equation:

0.05(10Q) + 0.10D + 0.25Q = 2.25

0.50Q + 0.10D + 0.25Q = 2.25

0.75Q + 0.10D = 2.25

We need to find the values of Q and D that satisfy this equation. From here, we can use algebraic techniques such as substitution or elimination to solve for Q and D.