A jar is full of 100 coins. All of the coins are either nickels or dimes. Suppose the value of the coins was $6.30. Explain how you can determine the number of each type of coin without solving another system of equations.

The first thing we should know is the value of each currency:

nickels = 0.05 $

dimes = 0.1 $

Let

x: number of nickels

y: number of dimes

We write the system of equations:

0.05x + 0.1y = 6.30

x + y = 100

To find the solution, you can graph both lines. The intersection between both lines is the number of nickels and dimes.

answer

Graph both lines in the same Cartesian plane and see where they intersect.

Let the number of nickels be x and that of dimes be y.

1 nickel=$0.05

1 dime=$0.1

total number of coins will be

x+y=100

⇒y=100-x ... i

total amount of money will be:

0.05x+0.1y=6.30 ... ii

substituting i in ii we get

0.05x+0.1 (100-x) = 6.30

0.05x+10-0.1x=6.30

-0.05x=-3.7

x=-3.7/-0.05=74

hence

y=100-74=26

Therefore we conclude that there was 74 nickels and 26 dimes.