Question 742999
Let d= number of dimes
n = number of nickels


"a total of 241 dimes and nickels"
hence d+n = 241
or n=241-d [1]


"he has $15.65 total in dimes and nickels"
The value of a nickel is $0.05 and a dime is $0.10
hence 0.10d+0.05n=15.65 or to express it in cents 10d+5n = 1565

=> n=(1565-10d)/5= 313 -2d [2]


Combining [1] and [2]
241-d=313-2d
=> d=313-241=72


Substituting in [1] gives n=241-72 = 169


Checking in [2], the total value of the coins = 5 x 169 + 10 x 72 = 1565c or $15.65