Question

You have 20 coins valued at 2.60. All are either quarters or nickels. Write and solve a system of equations to find the number of each coin you have.

Answer 1

The system of equations to determine the number of quarters (q) and nickels (n) is q + n = 20 and 25q + 5n = 260. Using the elimination method, we find there are 8 quarters and 12 nickels in the collection of 20 coins valued at $2.60.

Step-by-step explanation:

To find the number of quarters and nickels in a collection of coins that together are valued at $2.60, we can set up and solve a system of equations. Let's denote the number of quarters as q and the number of nickels as n.

The two equations to represent the situation are:

The total number of coins equation: q + n = 20

The total value equation in cents: 25q + 5n = 260

To solve this system of equations, we can use substitution or elimination method. Here, we will use the elimination method:

Multiply the first equation by 5 to align the nickel values: 5q + 5n = 100

Subtract this new equation from the total value equation: (25q + 5n) - (5q + 5n) = 260 - 100 which simplifies to 20q = 160

Divide by 20 to solve for q: q = 160 / 20 which simplifies to q = 8

Substitute q = 8 back into the first equation: 8 + n = 20 which simplifies to n = 12

There are 8 quarters and 12 nickels in the collection

Answer 2

To solve this problem you must apply the following proccedure:

1. You have a total of 21 coins, all nickels and dimes. Then:

x:nickels=5 cents

y: dimes=10 cents

x+y=21

2. You have that the total value is $1.70. Then:

5x+10y=170

3. The system of equation is:

x+y=21 (i)

5x+10y=170 (ii)

4. You have:

x+y=21

x=21-y

5(21-y)+10y=170

105-5y+10y=170

y=13 dimes

x+13=21

x=8 nickels