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? Set up the system and solve.

12 pennies, 3 nickles, and 2 dimes

p = number of pennies

n = number of nickles

d = number of dimes

p (1) + n (5) + d (10) = 47

that is, the number of pennies x 1 cent + number nickles x 5 cents

+ number of dimes x ten cents equals 47 cents

p = 4n

p + n + d = 17

Substituting 4n for p in the above

4n + n + d = 17

5n + d = 17

Subtract 5n from each side

d = 17 - 5n

We will now substitute 4n for p and (17-5n) for d in

the equation

p (1) + n (5) + d (10) = 47

4n (1) + n (5) + (17-5n) (10) = 47

9n + 170 - 50n = 47

-41n + 170 = 47

Subtract 170 from each side

-41n = 47 - 170

-41n = - 123

Divide each side by - 41

n = 3

Since p = 4n

p = 4 (3)

p = 12

Since p + n + d = 17

12 + 3 + d = 17

15 + d = 17

d = 2

So we have 12 pennies, 3 nickles and 2 dimes

12 + 3 (5) + 2 (10) ? = 47

12 + 15 + 20? = 47