Question

There are some Nichols dimes and quarters in a large piggy bank for every two nickels there a sweetheart forever to Diane's there in 5/4 there a 500 coins total how many nickels dimes and quarters are in the piggy bank explain your reasoning how much are the coins in the piggy bank worth

Answer 1

Question is not proper, Proper question is given below.

There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels, there are 3 dimes. For every 2 dimes, there are 5 quarters. There are 500 coins in all. How many nickels, dimes, and quarters are in the piggy bank? How much are the coins in the piggy bank worth all together?

Answer:

There are 80 nickels, 120 dimes and 300 quarters in the piggy bank.

The piggy bank is worth $91.

Explanation:

Let Number of Nickels be represented by 'n'.

Let Number of Dimes be represented by 'd'.

Let of Quarters be represented by 'q'.

Now Given:

For every 2 nickels, there are 3 dimes.

2 n = 3 d

1 n = number of dimes.

We will use Unitary method to find the same.

Number of 1 dimes d =
`(3)/(2)n`

Also Given:

For every 2 dimes, there are 5 quarters.

2 d = 5 q

1 d = number of quarters

We will use Unitary method to find the same.

Number of 1 quarter q =
`(5)/(2)d`

Also Given:

Total Number of coins = 500

`n+d+q=500`

Now d =
`(3)/(2)n`

AND q =
`(5)/(2)d = (5)/(2) *(3)/(2)n = (15)/(4)n`

So Substituting the values we get;

`n+(3)/(2)n+(15)/(4)n=500`

Taking LCM we get making denominator as 4.

`(4)/(4)n+(3*2)/(2* 2)n+(15* 1)/(4* 1)n=500\\\\(4)/(4)n+(6)/(4)n+(15)/(4)n=500\\\\(4n+6n+15n)/(4)=500\\\\\frac{25n}4 =500\\\\25n = 500* 4\\\\25n =2000\\\\n=(2000)/(25)=80`

Hence number of Nickels n = 80

Number of Dimes d =
`(3)/(2)n=(3)/(2) * 80 = 120`

Number of Quarters q =
`(15)/(4)n= (15)/(4) * 80 = 300`

Hence There are 80 nickels, 120 dimes and 300 quarters in the piggy bank.

Now we know that;

1 nickel = $0.05

so 80 nickels =
`0.05*80= $4`

1 dime = $0.1

so 120 dimes =
`0.1*120= $12`

1 quarter = $0.25

so 300 quarters =
`0.25*300= $75`

So Total money = $4+$12+$75 = $91

Hence the piggy bank is worth $91.