Respuesta :
Answer:
There are 3 nickels , 2 dimes and 12 pennies
Step-by-step explanation:
Let the no. of nickels be x
Now we are given that There are four times the number of pennies as nickels
So, No. of pennies = 4x
Let the no. of dimes be y
Now we are given that there are 17 coins
So, [tex]x+4x+y=17[/tex]
[tex]5x+y=17[/tex] ----A
Value of 1 nickel = $0.05.
value of x nickels = 0.05x
Value of 1 penny = $0.01.
Value of 4x pennies = 0.04 x
Value of 1 dime = $0.10
Value of y dimes= $0.10y
The value of the 17 coins is $0.47.
So, [tex]0.05x+0.04x+0.10y=0.47[/tex]
[tex]0.09x+0.10y=0.47[/tex] --- B
Substitute the value of y from A in B
[tex]0.09x+0.10(17-5x)=0.47[/tex]
[tex]0.09x+1.7- 0.5x=0.47[/tex]
[tex]-0.41x+1.7=0.47[/tex]
[tex]1.7-0.47=0.41x[/tex]
[tex]\frac{1.7-0.47}{0.41}=x[/tex]
[tex]3=x[/tex]
Substitute the value of x in 1
[tex]5(3)+y=17[/tex]
[tex]y=2[/tex]
So, no. of nickles =x= 3
No. of pennies = 4x = 4(3)=12
No. of dimes = y = 2
Hence there are 3 nickels , 2 dimes and 12 pennies
