Question

Chiara has 26 coins that equal 34 cents. All the coins are pennies, p, and nickels, n. How many nickels and pennies does Chiara have? Use the table to guess and check.

Answer 1

Explanation:

Sorry I'm late but the other person is wrong this is the answer

Answer 2

Chiara has 2 penny coins and 24 nickel coins

Explanation:

Let

p ----> the number of penny coins

n ---> the number of nickel coins

Remember that

`1\ penny=\$0.01`

`1\ nickel=\$0.05`

Chiara has 26 coins that equal 34 cents

so

`p+n=26`

isolate the variable x

`p=26-n` ----> equation A

34 cents=$0.34

`0.01p+0.05n=0.34`

Multiply by 100 both sides

`p+5n=34`

isolate the variable x

`p=34-5n` -----> equation B

Create a table to guess

assume different values of n and determine the value of p in equation A and equation B

The solution is when the value of p in the equation A must be equal to the value of p in equation B

1) For n=1

equation A

`p=26-1=25`

equation B

`p=34-5(1)=29`

`29\\eq 25`

2) For n=2

equation A

`p=26-2=24`

equation B

`p=34-5(2)=24\\24=24`

therefore

The solution is (2,24)

Chiara has 2 penny coins and 24 nickel coins