8. A school raffle sold 480 tickets. Students were charged $1/ticket and teachers $5/ticket. The total receipts were $560. How many of each ticket were sold? 9. An airplane travels 5432 km. On the outward trip it took 7 hours with the wind. On the return trip, it took 8 hours against the wind. What was the speed of the plane and the speed of the wind? (Remember: distance = speed x time)

8. Number of student tickets = 460

Number of teacher tickets = 100

9. Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr

Step-by-step explanation:

8.

Let number of students' tickets =

Let number of teachers' tickets =

Total number of tickets = 480

...... (1)

Price for one student's ticket = $1

Price for one teacher's ticket = $5

Total money collected by the tickets = $560

...... (2)

Subtracting (1) from (2):

By equation (1):

Number of student tickets = 460

Number of teacher tickets = 100

9.

Let the speed of airplane in still air = km/hr

Let the speed of air = km/hr

Total distance = 5432 km

Time taken with the wind = 7 hours.

Speed with the wind = km/h

Time taken against the wind = 8 hours.

Speed with the wind = km/h

Using the formula:

Distance = Speed Time

Adding (1) and (2):

By equation (1):

Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation:

answer: 8

step-by-step explanation: