360 people go on a school trip to one of four places.
Some of the information is shown in the table.
| | Adventure park | Botanic gardens | Wildlife centre | Red castle | Total |
|---|
| Boys | 65 | 12 | | 36 | |
| Girls | | 9 | 62 | | 163 |
| Staff | 15 | 3 | | | 37 |
| Total | 144 | 24 | 121 | 71 | 360 |
(a) Complete the table.
(b) Find the probability that
(i) a girl, picked at random, visits the Wildlife centre,
(ii) a person, picked at random from those visiting the Botanic gardens, is a girl,
(iii) a person, picked at random, visits the Adventure park or the Botanic gardens.
(c) The people who visit the Adventure park travel by coach. Each coach has 52 seats for passengers.
Complete this statement.
The least number of coaches needed for the trip to the Adventure park is …… and there will be a total of …… empty seats.
(d) The school hires one coach from each of two different companies for the trip to Red castle.
A coach from Fast Track coaches costs $600 plus $0.72 per kilometre travelled.
The total cost, in dollars, for travelling x kilometres is \( 600 + 0.72x \).
(i) A coach from Rapid coaches costs $550 plus $1.12 per kilometre travelled.
Write an expression for the total cost, in dollars, for travelling x kilometres.
(ii) Both companies charge the same amount for the trip.
Write down an equation and solve it to find the distance travelled.
(e) The length, \( l \) km, of the journey to the Wildlife centre is 53 km, correct to the nearest kilometre.
Complete this statement about the value of \( l \): $…… \leq l < ……$
(f) Samira takes $31.50 to spend in the Botanic gardens.
(i) She spends \( \frac{2}{7} \) of this money on food.
Work out how much Samira spends on food.
(ii) At the end of the visit to the Botanic gardens, Samira has $4.50 left.
What fraction of her money does Samira spend?
Give your answer in its simplest form.
