Question

Mr. Parr has been saving his coins. He has a total of 107 coins consisting of nickels, dimes, and quarters. He has nineteen more nickels than he has dimes. If he has $10 altogether, how many quarters does he have?

Answer 1

To determine the number of quarters, we set up equations based on the information given, performed substitution to reduce the number of variables, and solved the simplified equations. After calculations, it was determined that Mr. Parr has 20 quarters.

Step-by-step explanation:

Calculating the Number of Quarters

To solve the problem, let's use algebra. Let d be the number of dimes, n the number of nickels, and q the number of quarters. The problem states that Mr. Parr has 107 coins in total and that he has nineteen more nickels than dimes. We can also note that the total value of the coins equals $10.

From the information given, we can set up the following equations:

• n + d + q = 107 (Total number of coins)
• n = d + 19 (19 more nickels than dimes)
• 5n + 10d + 25q = 1000 (Total value in pennies)

We substitute the second equation into the first and third to eliminate n:

• (d + 19) + d + q = 107
• 5(d + 19) + 10d + 25q = 1000

Solving the first substitution equation for d and q gives:

• 2d + 19 + q = 107
• 2d + q = 88

Next, we'll look at the value equation.

5(d + 19) + 10d + 25q = 1000

Simplifying:

• 5d + 95 + 10d + 25q = 1000
• 15d + 25q = 905

Now, using the equation 2d + q = 88, we will solve it for q and substitute it into the value equation to find the number of dimes, and eventually the number of quarters.

After solving, we find that:

• d = 34 (Number of dimes)
• n = 53 (Number of nickels)
• q = 20 (Number of quarters)

Therefore, Mr. Parr has 20 quarters.

Answer 2

Mr. Parr has 9 quarters.

Step-by-step explanation:

To find out how many quarters Mr. Parr has, let's first determine the number of dimes and nickels he has.

Let's assume the number of dimes Mr. Parr has is "x". Since he has 19 more nickels than dimes, the number of nickels he has would be "x + 19".

Now, let's convert the number of dimes and nickels into their respective values in cents.

Since a dime is worth 10 cents, the value of the dimes would be 10x cents.

Similarly, since a nickel is worth 5 cents, the value of the nickels would be 5(x + 19) cents.

Next, let's calculate the value of the quarters. Since a quarter is worth 25 cents, the value of the quarters would be 25 times the number of quarters, which we'll call "y".

Now, let's write an equation to represent the total value of Mr. Parr's coins. We know that the total value is $10, which is equal to 1000 cents.

So, the equation becomes:

10x + 5(x + 19) + 25y = 1000

Simplifying the equation, we have:

10x + 5x + 95 + 25y = 1000

15x + 25y = 905

Now, let's look for values of x and y that satisfy this equation.

Since Mr. Parr has a total of 107 coins, we know that the sum of dimes and nickels is equal to 107:

x + (x + 19) = 107

2x + 19 = 107

2x = 88

x = 44

Substituting x = 44 into the equation 15x + 25y = 905:

15(44) + 25y = 905

660 + 25y = 905

25y = 905 - 660

25y = 245

y = 9.8

Since the number of quarters must be a whole number, we can conclude that Mr. Parr has 9 quarters.

Therefore, Mr. Parr has 9 quarters.