Answer:
Chiara has 2 penny coins and 24 nickel coins
Step-by-step explanation:
Let
p ----> the number of penny coins
n ---> the number of nickel coins
Remember that
[tex]1\ penny=\$0.01[/tex]
[tex]1\ nickel=\$0.05[/tex]
Chiara has 26 coins that equal 34 cents
so
[tex]p+n=26[/tex]
isolate the variable x
[tex]p=26-n[/tex] ----> equation A
34 cents=$0.34
[tex]0.01p+0.05n=0.34[/tex]
Multiply by 100 both sides
[tex]p+5n=34[/tex]
isolate the variable x
[tex]p=34-5n[/tex] -----> 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
[tex]p=26-1=25[/tex]
equation B
[tex]p=34-5(1)=29[/tex]
[tex]29\neq 25[/tex]
2) For n=2
equation A
[tex]p=26-2=24[/tex]
equation B
[tex]p=34-5(2)=24\\24=24[/tex]
therefore
The solution is (2,24)
Chiara has 2 penny coins and 24 nickel coins
