There are 107 coins in a jar, all dimes and nickels. The coins are worth $6.70. How many of each kind of coin is in the jar?

d = number of dimes

n = number of nickels

The jar contains a total of 107 coins, so

d + n = 107

Each dime is worth $0.10 and each nickel is worth $0.05, and the jar contains a total value of $6.70, so

0.10d + 0.05n = 6.70

Multiply both sides of the second equation by 100 to eliminate the decimal points:

10d + 5n = 670

Multiply both sides of the first equation by -5:

-5d - 5n = -535

Add the corresponding sides of these two equations to eliminate n and solve for d :

(10d + 5n) + (-5d - 5n) = 670 + (-535)

(10 - 5)d + (5 - 5)n = 670 - 535

5d = 135

d = 135/5 = 27

Then

n = 107 - d = 80

so the jar contains 27 dimes and 80 nickels.