If Jane has 27 coins, all nickels and dimes, that total $1.75, how many of each coin does she have?

Answer 1

Let N = # of nickels

D = # of dimes

Then:

N + D = 27 (27 coins in total)

5N + 10D = 175 (this represents the number of cents--each nickel is worth five cents, each dime ten cents).

I would use the substitution method here, because it is simple to isolate one of the variables in the 1st equation:

N = 27 - D

Now substitute that expression for N into the other equation (substitution method).

5(27 - D) + 10D = 175

135 - 5D + 10D = 175

5D = 40

D = 8

If D = 8, N = 27 - 8 = 19

19 nickels

8 dimes

-- 27 coins in total

Check:

19 nickels = 19(.05) = $0.95

8 dimes = 8(.10) = $0.80

$0.95 + $0.80 = $1.75

Answer 2

Answer 3

I have solved this word problem in this video. I hope you find this to be helpful. If you have any additional questions, please let me know.

Take care,

Dr. Christal-Joy Turner

Answer 4

n+d = 27 (Multiply this by -5)

5n + 10d = 175

-5n - 5d = -135

Add those two equations.

5d = 40

d = 8

Plug that back into the first equation.

n + 8 = 27

n = 27-8 = 19

19 nickels, 8 dimes