let

c = the number of cars

x = the cost of one car

s = the number of soldiers

y = the cost of one solder

Maddox spent $432 on some toy cars and soldiers

cx + sy = 432

the amount he spent on the soldiers is 3/5 the amount he spent on the cars

sy = (3/5)cx

the ratio of the number of soldiers to the number of cars is 1:6.

s : c = 1 : 6

c = 6s

each toy soldier costs $13 more than each toy car

y = x + 13

plug c = 6s and y = x + 13 into cx + sy = 432 and sy = (3/5)cx

6sx + s(x + 13) = 432

s(x + 13) = (3/5)6sx

subtract the first and the second equation

6sx + s(x + 13) - s(x + 13) = 432 - (3/5)6sx

6sx = = 432 - (3/5)6sx

sx = (5/48)432

sx = 45 plug into 6sx + s(x + 13) = 432 to find s

6sx + s(x + 13) = 432

6sx + sx + 13s = 432

7sx + 13s = 432

13s = 432 - 7sx

s = (1/13)(432 - 7*45)

s = 9 soldies

c = 6*9

c = 54 cars

Maddox bought 54 cars.