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.

25 dimes & 12 nickels

Step-by-step 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

12 nickel   25 dimes

Step-by-step 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

well there are two answers for that.

1: you need 120 ones then that will equal up to 120.

2: you could also do one 100 and 2 tens.

those are the answers that i have thought of.