Question

In a pot worth $2.35, there are 6 quarters, 5 dimes, 5 pennies, and the rest of the coins are nickels. What is the ratio of nickels to dimes?

Answer 1

Answer:

6:5 that is 6 nickels to 5 dimes.

Step-by-step explanation:

We have been given that in a pot worth $2.35, there are 6 quarters, 5 dimes, 5 pennies, and the rest of the coins are nickels.

We know that value of each quarter is $\ 0.25$, so value of 6 quarters would be $\ 0.25\times 6=\ 1.50$.

We know that value of each dime is $\ 0.10$, so value of 5 dimes would be $\ 0.10\times 5=\ 0.50$.

The value of each penny is $\ 0.01$, so the value of 5 pennies would be $\ 0.01\times 5=\ 0.05$.

Let us find the value of 6 quarters, 5 dimes, 5 pennies as:

$\ 1.50+\ 0.50+\ 0.05=\ 2.05$

Now, we will find the value of nickels by subtracting value of other coins from total value of all coins.

$\text{Value of nickels}=\ 2.35-\ 2.05$

$\text{Value of nickels}=\ 0.30$

We know that value of each nickel is $0.05. Now, we will divide $0.30 by $0.05 to find number of nickel coins as:

$\text{Number of nickel coins}=\frac{\ 0.30}{\ 0.05}$

$\text{Number of nickel coins}=6$

Since there are 6 nickels and 5 dimes, therefore, our required ratio would be $6:5$ that is 6 nickels to 5 dimes.

Answer 2

Answer:

6:5

Step-by-step explanation:

It is given that a pot worth $2.35 and there are 6 quarters, 5 dimes, 5 pennies, the rest of the coins are nickels.

We know that

$1 = 100 cents

1 penny = 1 cent = $0.01

1 nickel = 5 cents. = $0.05

1 dime = 10 cents. = $0.10

1 quarter = 25 cents = $0.25

The value of 6 quarters is

$6\times 0.25=1.50$

The value of 5 dimes is

$5\times 0.10=0.50$

The value of 5 pennies is

$5\times 0.01=0.05$

Let x be the number of nickels. So, the value of x nickels is

$x\times 0.05=0.05x$

Total value of 6 quarters, 5 dimes, 5 pennies, and x nickels is

$Total =1.50+0.50+0.05+0.05x$

$Total =2.05+0.05x$

It is given that the pot worth is $2.35.

$2.05+0.05x=2.35$

Subtract 2.05 from both sides.

$0.05x=0.30$

Divide both sides by 0.05.

$x=6$

The number of nickels is 5.

$\dfrac{Nickel}{Dimes}=\dfrac{6}{5}=6:5$

Therefore, the ratio of nickels to dimes is 6:5.