whats the answer for this I am very confused

Question

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 308 people entered the park, and the admission fees collected totaled 862.00 dollars. How many children and how many adults were admitted?

Answer 1

1.5C + 4A = 862

C + A = 308

multiply both sides by 1.5

1.5C +1.5A= 308(1.5) = 462

subtract last equation from the 1st

2.5A = 862-462 = 400

A = 400/2.5 = 160 adults

C = 308-160= 148 children

1.5(148) + 4(160) =222 + 640 = 862