Question

Bob has a coin collection made up of pennies and nickels if he has three times as many pennies as nickels and the total face value of the coins is $416 how many coins of each kind are in the collection

Answer 1

The value of a penny (in dollars) = 0.01

The value of a nickel (in dollars) = 0.05

Let the number of pennies Bob has be "p", and

Let the number of nickels Bob has be "n".

There are 3 times as many pennies as nickels. So we can write:

p = 3n

The total worth of all of the coins is 416, so we can write:

0.01p + 0.05n = 416

We have to solve these 2 equations for n and p. Putting first equation in 2nd, we get:

`\begin{gathered} 0.01p+0.05n=416 \\ 0.01(3n)_{}+0.05n=416 \\ 0.03n+0.05n=416 \end{gathered}`

Now, we solve for n:

`\begin{gathered} 0.03n+0.05n=416 \\ 0.08n=416 \\ n=(416)/(0.08) \\ n=5200 \end{gathered}`

Also, p = 3n

p = 3(5200)

p = 15,600

Hence,

There are

15,600 penny and 5200 nickels