When jim emptied his pockets he found 19 coins consisting of only nickels and dimes with a total value of $1.55. how many of each coin does he have?

Let's let n = the number of nickels in his pocket, and d=the number of dimes in his pocket. Nickels are worth. 05 and dimes are worth. 10.

Now, we can write two equations using these variables and solve them as a system of equations:

n+d=19 [the number of nickels and dimes equals 19]

.05n+.10d=1.55 [the values of nickels and dimes times their quantities equals $1.55]

100 (.05n+.10d=1.55) [multiply second equation by 100 to eliminate decimals]

5n+10d=155

5 (n+d=19) [multiply first equation by 5 so the 'n' terms have the same coefficient]

5n+5d=95

Now subtract the equations to eliminate n and simplify to solve for d:

5n+10d=155

(-)

5n+5d=95

5d=60

d=12. There are 12 dimes

Now substitute into the simpler equation to find number of nickels:

n + (12) = 19

n=7. There are 7 nickels.

Check your work:

12 (.10) + 7 (.05) = 1.20 +.35 = $1.55