Question
Burton City is a football team.
(a) Burton City has 1732 supporters who want to travel to the next game.
The football club hires some buses.
Each bus seats 52 supporters.
(i) Work out the number of buses needed to take these supporters to the game.
(ii) The cost of the buses will be shared equally amongst these supporters.
Each bus costs $198 to hire.
Work out the amount that each supporter must pay.
Give your answer correct to the nearest 10 cents.
$ ……………………..
(b) Adam and Mabel are two supporters.
The scale drawing shows the positions of Adam’s home, A, and Mabel’s home, M.
The scale is 1 centimetre represents 500 metres.
(i) Work out the distance in kilometres from A to M.
…………………………………….. km
(ii) Burton City’s football ground is on a bearing of 105° from A and on a bearing of 068° from M.
Mark the position of the football ground on the scale drawing.
(c) Teams are given points for winning or drawing games.
A win is given w points and a draw is given d points.
No points are given when the team loses.
(i) Burton City has 24 points after winning 2 games and drawing 5 games.
Complete the equation.
2w + 5d = ………………..
(ii) Sowton Rovers is another football team.
Sowton Rovers has 29 points after winning 3 games and drawing 4 games.
Write this information as an equation.
………………………………….. = ………………………..
(iii) Solve your two equations to find the number of points for a win and the number of points for a draw.
You must show all your working.
w = ………………………………………….
d = ………………………………………….
(iv) Another team, Cranbrook United, has played 12 games.
It has won 4 games, drawn 5 games and lost 3 games.
Work out the number of points Cranbrook United has after 12 games.
Answer/Explanation
Ans:
(a) (i) 34
(ii) 3.90
(b) (i) 3.9
(ii) football ground indicated in
correct position
(c) (i) 24
(ii) 3w + 4d = 29
(iii) [w] 7
[d] 2
(iv) 38
Question
Mr and Mrs Clark and their three children live in the USA and take a holiday in Europe.
(a) Mr Clark changes \(\$500\) into euros when the exchange rate is euro 1= \(\$1.4593\).
Calculate how much he receives.
Give your answer correct to 2 decimal places.
(b) Tickets for an amusement park cost €62 for an adult and €52 for a child.
Work out the cost for Mr and Mrs Clark and their three children to visit the park.
(c) Mr Clark sees a notice:
(d) Mrs Clark buys 6 postcards at €0.98 each.
She pays with a €10 note.
Calculate how much change she will receive.
(e)Children under a height of 130 cm are not allowed on one of the rides in the park.
Helen Clark is 50 inches tall.
Use 1 inch = 2.54 cm to show that she will not be allowed on this ride.
Answer/Explanation
(a) euro 1=\(\$1.4593\)
using unitary method,
\(\$1.4593\)=euro 1
Therefore, \(\$500\)= \(\frac{1}{1.4593}\times 500\)
= 342.6300
After rounding it off to 2 decimal places,
324.63
(b) Tota cost= 3. (cost for child)+(2. cost for adult)
= 3.(52)+2.(62)
=156+124
=280 euro
(c) Percentage=\(\frac{Actual cost}{Calculated cost}\times 100\)
= \(\frac{200}{280}\times 100\)
= 71.4
(d) Total cost of postard = 6\(\times\)0.98
= \(5.88 euro\)
Change she will receive = \(10 euro\)- \(5.88 euro\)
= \(4.12 euro\)
(e) Height in cm of Helen clark :
1 inch = 2.54 cm
So, 50\(\times \) 2.54cm
= 127.00 cm
Therefore, the height of Helen Clark is 127 cm
As , her height is 127 cm which is less than 130cm , So she would not be allowed in the park