Respuesta :
Answer:
She have 53 type of quarters and 27 type of nickels.
Step-by-step explanation:
Given:
Sam has a jar contain 80 coins, all of which are either quarters or nickels.
The total value of quarters and nickels is $14.60.
Now, to get each type of coin she have.
Let the number of quarters be [tex]x.[/tex]
And let the number of nickels be [tex]y.[/tex]
So, total number of coins:
[tex]x+y=80[/tex]
[tex]y=80-x\ \ \ ....(1)[/tex]
Now, the total value of coins:
[tex]0.25(x)+0.05(y)=14.60[/tex]
Substituting the value of [tex]y[/tex] from equation (1):
[tex]0.25(x)+0.05(80-x)=14.60[/tex]
[tex]0.25x+4-0.05x=14.60[/tex]
[tex]0.20x+4=14.60[/tex]
Subtracting both sides by 4 we get:
[tex]0.20x=10.60[/tex]
Dividing both sides by 0.20 we get:
[tex]x=53.[/tex]
The number of quarters = 53.
Now, to get the number of nickels by substituting the value of [tex]x[/tex] in equation (1):
[tex]y=80-x\\\\y=80-53\\\\y=27.[/tex]
The number of nickels = 27.
Therefore, she have 53 type of quarters and 27 type of nickels.
