Question

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)

Answer 1

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

Explanation:

8.

Let number of students' tickets =
`x`

Let number of teachers' tickets =
`y`

Total number of tickets = 480

`x+y=480` ...... (1)

Price for one student's ticket = $1

Price for one teacher's ticket = $5

Total money collected by the tickets = $560

`x +5y = 560` ...... (2)

Subtracting (1) from (2):

`4y = 80\\\Rightarrow y = 20`

By equation (1):

`x = 460`

Number of student tickets = 460

Number of teacher tickets = 100

9.

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

Let the speed of air =
`v` km/hr

Total distance = 5432 km

Time taken with the wind = 7 hours.

Speed with the wind =
`u+v` km/h

Time taken against the wind = 8 hours.

Speed with the wind =
`u-v` km/h

Using the formula:

Distance = Speed
`*` Time

`5432 = (u+v)* 7\\\Rightarrow u +v = 776 .... (1)`

`5432 = (u-v)* 8\\\Rightarrow u - v = 679 .... (2)`

Adding (1) and (2):

`2u = 1455\\\Rightarrow u = 727.5\ km/hr`

By equation (1):

`v = 48.5\ km/hr`

Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr