Question

You have 17 coins in pennies, nickels, and dimes in

your pocket. The value of the coins is $0.47. There are four times the number of pennies as nickels. How many
of each type of coin do you have?

Answer 1

7 pennies 4 nickels 2 dimes

Answer 2

There are 3 nickels , 2 dimes and 12 pennies

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,
`x+4x+y=17`

`5x+y=17` ----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,
`0.05x+0.04x+0.10y=0.47`

`0.09x+0.10y=0.47` --- B

Substitute the value of y from A in B

`0.09x+0.10(17-5x)=0.47`

`0.09x+1.7- 0.5x=0.47`

`-0.41x+1.7=0.47`

`1.7-0.47=0.41x`

`(1.7-0.47)/(0.41)=x`

`3=x`

Substitute the value of x in 1

`5(3)+y=17`

`y=2`

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