Question

A pile of 37 coins consists of nickels and dimes. The total value

of the coins is $3.10. Find the number of each type of coin.

Answer 1

12 nickel 25 dimes

Explanation:

n=nickels

d=dimes

I'll multiply by 100 the value of the coins to avoid decimals

n + d = 37

5n + 10d = 310

Now Multiply the first row by 10 (to cancel dime )

10n +10 d = 370

5n+ 10d = 310

Subtract the second from the first:

5n = 60

n=12

12 nickels 25 dimes

0.05*12 = 0.60

0.10 *25 = 2.5

0.60 +2.5 = 3.10

Answer 2

25 dimes & 12 nickels

Explanation:

Let there be "n" nickels and "d" dimes

Total, there are 37 of them, so we can write:

n + d = 37

Also, valueof nickel is 0.05 and value of dime is 0.10 (in dollars) and total value of these 37 coins is 3.10, so we can write:

0.05n + 0.10d = 3.10

Now we can write first equation as:

n + d = 37

n = 37 - d

Replace this into equation 2 and solve for d:

0.05n + 0.10d = 3.10

0.05(37 - d) + 0.10d = 3.10

1.85 - 0.05d + 0.10d = 3.10

0.05d = 3.10 - 1.85

0.05d = 1.25

d = 1.25/0.05

d = 25

Now, n = 37 - d, n = 37 - 25 = 12

So,

There are 25 dimes & 12 nickels