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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)

Respuesta :

isyllus

Answer:

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 = [tex]x[/tex]

Let number of teachers' tickets = [tex]y[/tex]

Total number of tickets = 480

[tex]x+y=480[/tex] ...... (1)

Price for one student's ticket = $1

Price for one teacher's ticket = $5

Total money collected by the tickets = $560

[tex]x +5y = 560[/tex] ...... (2)

Subtracting (1) from (2):

[tex]4y = 80\\\Rightarrow y = 20[/tex]

By equation (1):

[tex]x = 460[/tex]

Number of student tickets = 460

Number of teacher tickets = 100

9.

Let the speed of airplane in still air = [tex]u[/tex] km/hr

Let the speed of air = [tex]v[/tex] km/hr

Total distance = 5432 km

Time taken with the wind = 7 hours.

Speed with the wind = [tex]u+v[/tex] km/h

Time taken against the wind = 8 hours.

Speed with the wind = [tex]u-v[/tex] km/h

Using the formula:

Distance = Speed [tex]\times[/tex] Time

[tex]5432 = (u+v)\times 7\\\Rightarrow u +v = 776 .... (1)[/tex]

[tex]5432 = (u-v)\times 8\\\Rightarrow u - v = 679 .... (2)[/tex]

Adding (1) and (2):

[tex]2u = 1455\\\Rightarrow u = 727.5\ km/hr[/tex]

By equation (1):

[tex]v = 48.5\ km/hr[/tex]

Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr

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