Apps. and Interpretation for IBDP Maths Ebook 1 | Page 60

Your Practice Set – Applications and Interpretation for IBDP Mathematics
16
Paper 1 – Systems
Example
The total profit $y of selling plastic boxes can be modelled by the equation
2
y � ax �bx � c , where x is the number of plastic boxes ordered from a factory, and a ,
b and c are real numbers. The total profits of selling 100 plastic boxes, 200 plastic boxes
and 400 plastic boxes are $122, $424 and $1628 respectively.
(a) (i) Show that 10000a �100b � c � 122 .
(ii) Show that 40000a � 200b � c � 424 .
(iii) Write down the third equation in a , b and c .
(b) Hence, find the values of a , b and c .
[3]
[4]
Solution
(a)
(i)
2
122 (100) (100)
� a �b � c
A1
10000a �100b � c � 122
AG N0
(ii)
2
424 (200) (200)
� a �b � c
A1
40000a � 200b � c � 424
AG N0
(b)
(iii) 160000 a � 400b �c
� 1628
A1 N1
�10000a �100b � c �122
�
�40000a � 200b � c � 424
�
�160000a � 400b � c �1628
1
a � ,
100
1
b � and c � 20
A3 N4
50
(M1) for valid approach
[3]
[4]
50
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