Question

There are $3.90 worth of nickles and quarters in a piggy bank. There are 6 more quarters than nickels. How many of each coin are in the piggy bank?

Answer 1

Answer:

8 nickels, 14 quarters

Step-by-step explanation:

First let us know the conversions of the units:

1 dollar = 4 quarters

1 dollar = 20 nickels

1 quater = 5 nickels

Let the number of nickels = x

Let the number of quarters = y = x + 6 (given that quarters are 6 more than the number of nickels)

So, the number of quarters y = (x + 6) x 5 nickels — eq(1)

x + y = $ 3.90

=> x + y = 3.90 (20) nickels

=> x + [(x + 6) x 5] = 78

=> x + 5x + 30 = 78

=> 6x = 48

=> x = 8 nickels

Also,

y = x + 6 = 8 + 6 = 14 quarters.

There are

8 nickels + 14 quarters = $3.90

Given; quarters are 6 more than nickels.

Now, let us check the solution.

1 dollar - 4 quarters

? Dollars - 14 quarters

= (14 x 1)/4

= $3.5

1 dollar - 20 nickels

? Dollars - 8

= (8 x 1)/20

= $0.4

$3.5 + $0.4 = $3.90

Answer 2

Answer:

8 nickels and 14 quarters

Step-by-step explanation:

In this question,

We have been given that,

Quarters are 6 more than nickels.

We know the conversion rates

1 dollar = 4 quarters

1 dollar = 20 nickels

1 quarter = 5 nickels

Let the number of nickels = x

Let the number of quarters = y

                                             = x + 6

So, the number of quarters y = (x + 6) x 5 nickels — (as 1 quarter                   = 5 nickels)

x + y = 3.90

x + y = 3.90 (5 × 4) nickels

x + [(x + 6) x 5] = 78

x + 5x + 30 = 78

6x = 48

x = 8 nickels

Also,

y = x + 6 = 8 + 6 = 14 quarters.

Hence, There are  

8 nickels + 14 quarters = $3.90