Answer:
The coins of each type are, 17 nickel coins and the 5 quarter coins.
Step-by-step explanation:
Given:
Liliana has $2.10 in nickels and quarters in her purse.
She has 12 more nickels than quarters.
Now, to find the coins of each type she have.
Let the number of nickels be [tex]x.[/tex]
Let the number of quarters be [tex]x-12.[/tex]
The total worth of coins = $2.10.
The value of a quarter is $0.25 and the value of a nickel is $0.05.
According to question:
[tex]0.25(x-12)+0.05(x)=2.10[/tex]
⇒ [tex]0.25x-3+0.05x=2.10.[/tex]
⇒ [tex]0.30x-3=2.10[/tex]
Adding both sides by 3 we get:
⇒ [tex]0.30x=5.10[/tex]
Dividing both sides by 0.30 we get:
⇒ [tex]x=17.[/tex]
The number of nickels = 17.
Now, to get the number of quarters we put value of [tex]x[/tex] :
[tex]x-12[/tex]
[tex]=17-12=5.[/tex]
The number of quarters = 5.
Therefore, the coins of each type are, 17 nickel coins and the 5 quarter coins.
