Sam found a #of nickels, dimes, and quarters in his room.?

Question

He found 3 more dimes than nickels but twice as many quarters than dimes. The total value of the coins was $5.05, How many coins of each type did Sam find?

Answer 1

Using n for nickels, d for dimes, q for quarters, you have three equations:

n = d - 3
q = 2d
5n + 10d + 25q = 505 (in cents)

Each of the first two handily lets you replace a different variable with d in the third equation so substitute:

5n + 10d + 25q = 505
5(d-3) + 10d + 25(2d) = 505
5d - 15 + 10d + 50d = 505
65d = 520
d = 8

That gives 8 dimes.

Now you can use each of the first two equations:

n = d - 3
n = 8 - 3
n = 5

q = 2d
q = 2*8
q = 16

And you have 5 nickels, 8 dimes, and 16 quarters.

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To check, see if the total money is right:

5 nickels are worth $0.25
8 dimes are worth $0.80
16 quarters are worth $4.00

$4.00 + $0.25 + $0.80 = $5.05

Answer 2

sam found 5 nickles, 8 dime and 16 quarters

Answer 3

5.05 = .05x + .1 (x + 3) + .25 (2x +6), so .65x + 1.80 = 5.05, or
.65x = 3.25, and x = 5.
nickles = 5 ($.25)
dimes = 8 ($.80)
quarters = 16 ($4.00)