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

Answer:

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

All coins in the piggy bank worth $91.

Step-by-step explanation:

Please consider the complete question:

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 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?

Let n, d, q represent number of nickles, dimes and quarters respectively.

For every 2 nickels there are 3 dimes. We can represent this information in an equation as:

$\frac{2}{n}=\frac{3}{d}...(1)$ or

$n=\frac{2d}{3}...(1)$

For every 2 dimes there are 5 quarters. We can represent this information in an equation as:

$\frac{2}{d}=\frac{5}{q}...(2)$ or  

$q=\frac{5d}{2}...(2)$  

There are 500 coins total. We can represent this information in an equation as:

$n+d+q=500...(3)$

We will use substitution method to solve our given system.

Upon substituting equation (1) and equation (2) in equation (3), we will get:

$\frac{2d}{3}+d+\frac{5d}{2}=500$  

Multiply the equation by 6:

$\frac{2d}{3}*6+d*6+\frac{5d}{2}*6=500*6$  

$2d*2+6d+5d*3=3000$  

$4d+6d+15d=3000$  

$25d=3000$  

$\frac{25d}{25}=\frac{3000}{25}$  

$d=120$  

Therefore, there are 120 dimes in the piggy bank.

Upon substituting $d=120$ in equation (1), we will get:

$n=\frac{2(120)}{3}$

$n=2(40)$

$n=80$

Therefore, there are 80 nickels in the piggy bank.

Upon substituting $d=120$ in equation (2), we will get:

$q=\frac{5d}{2}$  

$q=\frac{5(120)}{2}$  

$q=5(60)$  

$q=300$  

Therefore, there are 300 quarters in the piggy bank.

Now, we need to find the value of all coins.

We know 1 quarter is worth $0.25, so 300 quarters will be worth $\ 0.25\times 300=\ 75$.

We know 1 dime is worth $0.10, so 120 dimes will be worth $\ 0.10\times 120=\ 12$.

We know 1 nickel is worth $0.05, so 80 nickels will be worth $\ 0.05\times 80=\ 4$.

$\text{All coins worth}=\ 75+\ 12+\ 4$

$\text{All coins worth}=\ 91$

Therefore, all coins in the piggy bank worth $91.