Total income = Average income × Number of members = 5000 × 4 = $20000.

Current total age = 5 + 10 + 15 = 30. To maintain an average of 10 with 4 children, total age must be 40. Therefore, the new child's age must be 40 - 30 = 10.

Total cost = Average cost per person × Number of people = 20 × 5 = $100.

Let the score in the fourth subject be x. The average is (60 + 70 + 80 + x) / 4 = 75. Solving gives x = 85.

Total percentage score = Average percentage × Number of students = 85% × 20 = 1700%.

Total score = 85 × 20 + 95 = 1700 + 95 = 1795. New average = 1795 / 21 = 85.95, which rounds to 86.

Total = Average × Number of items = 50 × 10 = 500.

Total = Average × Number of items = 50 × 8 = 400.

Sum of the numbers = Average × Number of items = 30 × 5 = 150.

Let the integers be (x-1), x, and (x+1). Their average is (x-1 + x + x+1) / 3 = x.

Let the number of boys be x and the number of girls be 30 - x. The total score of boys is 80x and that of girls is 70(30 - x). The overall average is given by (80x + 70(30 - x)) / 30 = 75. Solving this gives x = 15.

Distance = Speed × Time = 10 km/h × 2 h = 20 km.

Distance = Speed × Time = 12 km/h × 2 h = 24 km.

New total age = (30 × 10) - 40 = 260. New average = 260 / 9 = 28.89, which rounds to 29.

Total age = 40 × 10 = 400. New total age = 400 - 60 = 340. New average = 340 / 9 = 37.78, which rounds to 38.

Let the integers be x, x+1, x+2. The average is (x + (x + 1) + (x + 2)) / 3 = 20. Solving gives x = 18.