Analysis and Approaches for IBDP Maths Ebook 2 | Page 46

Your Practice Set – Analysis and Approaches for IBDP Mathematics
2. 8400 citizens attended a concert. Let x , y and z be the number of children, the number
of adults and the number of elderly people attending the concert respectively. It is also
given that the sum of the number of children and the number of elderly people is less than
the number of adults by 6288.
(a) Write down two equations in x , y and z .
[2]
The cost of a child ticket, an adult ticket and an elderly ticket were set to be $42, $84 and
$21 respectively. The total cost of tickets sold in the concert was $655872.
(b) Find the values of x , y and z .
[3]
3. The total price $P of selling x apples, y oranges and z pears can be modelled by
P � ax �by � cz , where a , b and c are the unit prices of apples, oranges and pears
respectively. The following table shows the total prices of different combinations of
apples, oranges and pears:
$P x y z
$150 10 12 13
$178 14 8 19
$230 22 23 7
(a) Find the values of a , b and c .
(b)
Find the total price of 30 apples and 35 pears.
[4]
[2]
4. In a football league, each team gains x points for a win, y points for a draw and z
points for a loss. There are 46 matches in a year. The following table shows the
performances of three teams in 2019:
Team Win Draw Loss Points
A 30 16 0 152
B 23 15 8 114
C 11 17 18 60
(a) Find the values of x , y and z .
(b) Interpret the meaning of z .
[4]
[1]
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