let

d = destination charge

m = major options package

b = base price

with the major options package and destination charge, a sports car costs $24,416

b + m + d = 24416

the base price of the car was ten times the price of the major options package

b = 10*m => m = b/10

the base price of the car was fifty times the destination charge

b = 50*d => d = b/50

substituting for m and d in b + m + d = 24416 we get

b + b/10 + b/50 = 24416

multiply through by 50 to eliminate fractions

50b + 5b + b = 50*24416

56b = 50*24416

Divide both sides by 56 to find b

b = 50*24416/56

b = $21,800

the base price of the car is $21,800.