Mary Jo has $4.15 worth of nickels, dimes, and quarters. The number of nickels is 3 more than the number of dimes. The number of quarters is 8 more than the number of dimes. How many of each coin does she have? ( Hint : Let x = the number of dimes.)
A) 9 nickels, 6 dimes and 14 quarters
B) 13 nickels, 10 dimes and 18 quarters
C) 7 nickels, 4 dimes and 12 quarters
D) 8 nickels, 5 dimes and 13 quarters
E) 4 nickels, 1 dimes and 9 quarters

Question

Quizplus · Accepted Answer

Let x be the number of dimes, then:

Number of nickels = x + 3
Number of quarters = x + 8

Value of nickels = 0.05(x+3) = 0.05x + 0.15
Value of dimes = 0.10x
Value of quarters = 0.25(x+8) = 0.25x + 2.00

Total value of coins = $4.15

0.05x + 0.10x + 0.25x + 2.15 = 4.15
0.40x = 2.00
x = 5

Therefore, Mary Jo has:
- 8 nickels (x+3=5+3=8)
- 5 dimes (x=5)
- 13 quarters (x+8=5+8=13)

The total value of these coins is:

8(0.05) + 5(0.10) + 13(0.25) = $2.00 + $0.50 + $3.25 = $4.75

Since the total value of the coins matches the given value of $4.15, this is the correct answer.

Mary Jo Has $4