Help with work please

Question

1. On a certain hot​ summer's day, 467 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $856.25. How many children and how many adults swam at the public pool that​ day?
2. The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 500 people. By selling​ tickets, the members would like to raise $2,850 every night to cover all expenses. Let d represent the number of adult tickets sold at $7.50. Let s represent the number of student tickets sold at ​$4.50 each. If all 500 seats are filled for a​ performance, how many of each type of ticket must have been sold for the members to raise exactly $2,850​? At one performance there were three times as many student tickets sold as adult tickets. If there were 480 tickets sold at that​ performance, how much below the goal of ​$2,850 did ticket sales​ fall?

Answer 1

C+A = 467

multiply both sides by 1.25

1.25C +1.25A = 1.25(467)

1.25C + 2.5A = 856.25

1.25C +1.25A = 1.25(467)

subtract last 2 equations above to eliminate one variable

2.5A - 1.25A = 856.25 - 583.75 = 272.5

1.25A = 272.5

A = 272.5/1.25 = 218 adults

C =467-218 = 249 children

check the answer

1.25(249) + 2.5(218) = 311.25+545= 856.25

s + d = 500

7.5s +7.5d = 7.5(500) = 3750

4.5s + 7.5d = 2850

7.5s -4.5s =3750-2850 = 900

3s =900

s =900/3 = 300 students

d =500-300=200 adults

4.5(300) + 7.5(200) = 1350+1500 = 2850

s = 3d

s+d =480

3d +d = 480

4d = 480

d=480/4 = 120 students

s=360 adults

4.5(360) + 7.5(120) = 1620 + 900 = 2520

2850-2520 = $330 short of the goal