Aman has a collection of dimes and nickels with a total value of $1.70. if he has 8 more dimes than nickels how many of each coin does he have?

Step-by-step explanation:

We first have to write an expression for each of the types of coins in terms of one of them.  If he has 8 more dimes than nickels, let's call nickels "x".  That means that dimes is "x + 8".  The value of a nickel is .05, so the expression relating the number of nickels to the worth of the nickel is .05x.  The value of a dime is .10, so the expression relating the number of dimes to the worth of the dime is .10(x + 8).  The total value of these coins is 1.70:

.05x + .10(x + 8) = 1.70 and

.05x + .10x + .8 = 1.70 and

.15x = .9 so

x = 6

That means we have 6 nickels and 14 dimes.