Answer:
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.