Question

Serenity has $0.46 worth of pennies and nickels. She has a total of 14 pennies and nickels altogether. Determine the number of pennies and the number of nickels that Serenity has.

Answer 1

The number of pennies are 6 and number of nickels are 8.

Explanation:

Given:

Serenity has $0.46 worth of pennies and nickels.

She has a total of 14 pennies and nickels altogether.

Now, to find the number of pennies and the number of nickels she has.

Let the number of pennies be
`x`.

And the number of nickels be
`y`.

So, the number of pennies and nickels altogether are:

`x+y=14.`

`x=14-y.`........( 1 )

As given total worth = $0.46.

And the value of a penny is $0.01 and the value of a nickel is $0.05.

Now, the total worth of pennies and nickels:

`0.01x+0.05y=0.46`

Putting the value of equation ( 1 ) in the place of
`x`.

`0.01(14-y)+0.05y=0.46`

`0.14-001y+0.05y=0.46`

`0.14+0.04y=0.46`

Subtracting both sides by 0.14 we get:

`0.04y=0.32`

Dividing both sides by 0.04 we get:

`y = 8.`

So, the number of nickels = 8.

Now, putting the value of
`y` in equation ( 1 ) we get:

`x=14-8`

`x=6.`

Thus, the number of pennies = 6.

Therefore, the number of pennies are 6 and number of nickels are 8.