Lucky found $8.25 in pennies, nickels, dimes, and quarters while walking home from school one week. When she deposited this money in the bank, she noticed that she had twice as many nickels as pennies, 1 fewer dime than nickels, and 1 more quarter than nickels. How many quarters did Lucky find that week?
The correct answer is D.
Let p = the number of pennies, n = the number of nickels, d = the number of dimes, and q = the number of quarters. Each of these variables can be expressed in terms of a common variable - in this case, p.
Lucky had p pennies, so the value of the pennies was p cents. Because she had twice as many nickels as pennies, n = 2p, and the value of the nickels was 5(2p) cents. She had 1 fewer dime than nickels, so d = n - 1 = 2p - 1, and the value of the dimes was 10(2p - 1) cents. Finally, she had 1 more quarter than nickels, so q = n + 1 = 2p + 1, and the value of the quarters was 25(2p + 1) cents.
Because the total value of the coins is $8.25, or 825 cents, p satisfies the following equation:
p + 5(2p) + 10(2p - 1) + 25(2p + 1) = 825
p + 10p + 20p - 10 + 50p + 25 = 825
81p + 15 = 825
81p = 810
Therefore, p = 10
So, q = 2p + 1 = 2(10) + 1 = 21 quarters.