Mark has some nickels, dimes, and quarters in his pocket. he has three times as many quarters as nickels. he has five more dimes than nickels. the total amount he has in his pocket is $5. how many of each coin does he have

15 quarters
10 dimes
5 nickels

five more dimes than nickels means we know there is at least 5 dimes, or 50 cents
if we subtract this from $5, we have $4.50.
With those 5 dimes gone, the number of dimes equals the number of nickels. If there are 3 times as many quarters as nickels, there are also 3 times as many quarters as dimes. So for every 3 quarters (0.75), there is one dime (0.10) and one nickel (0.05).
0.75 + 0.10 + 0.05 = 0.90
you find the number of remaining coins by dividing the total minus the 5 dimes (4.50) by 0.90.
4.50 ÷ 0.90 = 5
this is how many times 3 quarters, one dime, and one nickel go into 4.50
so, the answer to how many of each coin is:
3 quarters × 5 = 15 quarters
one dime × 5 = 5 plus the original 5 we took out = 10 dimes
one nickel × 5 = 5 nickels

to check
5.00 = 15(0.25) + 10(0.10) + 5(0.05)
5.00 = 3.75 + 1.00 + 0.25
5.00 = 5.00 ✔

Really long apparently