Question

Ian has $0.81 worth of pennies and nickels. He has a total of 21 pennies and nickels altogether. Write a system of equations that could be used to determine the number of pennies and the number of nickels that Ian has. Define the variables that you use to write the system.

Answer 1

Equations that could be used to determine the number of pennies and the number of nickels that Ian has is Nx +Py = 0.81

Explanation:

Given:

Total worth of pennies and nickels = $0.81

Total number of pennies and nickels = 21

To Find:

System of equations that could be used to determine the number of pennies and the number of nickels that Ian has

Solution:

Let

The number of pennies be x

The number of nickel be y

The cost of one penny be P

The cost of one Nickel be N

Total number of pennies and nickels altogether = 21

so

x+y =21------------------------------(1)

from (1)

x= y-21--------------------------------(2)

Now the total worth of pennies and nickels = $0.81

(cost of 1 penny X number of pennies) + (cost of 1 nickel X number of nickels) = 0.81

`(P * x ) + (N * y ) = 0.81`

`(Px ) + (Ny) = 0.81`

`(P * (y-21) ) + (N * y ) = 0.81`

`Py-21P + Ny = 0.81`

`Py + Ny -21P = 0.81`-----------------(3)