Nickels = N
Dimes = D
Nickels are worth 5 cents, written as 0.05
Dimes are worth 10 cents, written as 0.10
We have N +D = 20 ( Nickels plus dimes = 20 coins)
We also have 0.05N + 0.10D = 1.40 ( the total price of nickels plus total price of dimes.
N +D = 20 can be re-written as N = 20-D
Replace N with the re-written equation in the 2nd equation:
0.05(20-D) + 0.10D = 1.40
Distribute the 0.05:
1-0.05D + 0.10D = 1.40
Combine the like terms: -0.05D +0.10D = 0.05D
So now you have:
1 + 0.05D = 1.40
Subtract 1 from each side:
0.05D = 0.40
Divide both sides by 0.05:
D = 0.40 / 0.05
D = 8
They have 8 dimes.
They had 20 coins total so the number of nickels is 20 - 8 = 12 nickels.
8 dimes = 8 x 0.10 = 0.80 ( 80 cents)
12 nickels = 12 x 0.05 = 0.60 ( 60 cents)
0.80 + 0.60 = 1.40
There are 12 nickels.
