Answer: Phil has 33 dimes, and 17 nickels
Explanation:
Let number of nickels be X, and dimes be Y.
X + Y = 50.
Since nickels stand for 5 cents, or 0.05 dollars, and dimes are 10 cents, or 0.10 dollars, we can also write the total worth as:
0.05*X + 0.10*Y = 4.15
Multiply this last equation by 20:
20*0.05*X + 20*0.10*Y = 20*4.15
Simplify:
X + 2*Y = 83
Subtract the first equation (X + Y = 50) from this one:
Y = 33.
Thus Phil has 33 dimes, and 17 nickels.