Aperson has 20 coins, all nickels and dimes, worth one dollar and 40 cents. how many nickels are there

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.

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step-by-step explanation:

step-by-step explanation:

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