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.

Step-by-step 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 = $\frac{3}{2}n$

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 = $\frac{5}{2}d$

Also Given:

Total Number of coins = 500

$n+d+q=500$

Now d = $\frac{3}{2}n$

AND q = $\frac{5}{2}d = \frac{5}{2} \times\frac{3}{2}n = \frac{15}{4}n$

So Substituting the values we get;

$n+\frac{3}{2}n+\frac{15}{4}n=500$

Taking LCM we get making denominator as 4.

$\frac{4}{4}n+\frac{3\times2}{2\times 2}n+\frac{15\times 1}{4\times 1}n=500\\\\\frac{4}{4}n+\frac{6}{4}n+\frac{15}{4}n=500\\\\\frac{4n+6n+15n}{4}=500\\\\\frac{25n}4 =500\\\\25n = 500\times 4\\\\25n =2000\\\\n=\frac{2000}{25}=80$

Hence number of Nickels n = 80

Number of Dimes d = $\frac{3}{2}n=\frac{3}{2} \times 80 = 120$

Number of Quarters q = $\frac{15}{4}n= \frac{15}{4} \times 80 = 300$

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  = $0.05\times80= 4$

1 dime = $0.1

so 120 dimes = $0.1\times120= 12$

1 quarter = $0.25

so 300 quarters = $0.25\times300= 75$

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

Hence the piggy bank is worth $91.