Question 7 — IGCSE 0580 Oct/Nov 2024 Paper 41
Cambridge IGCSE Mathematics 0580, Extended tier, calculator. Topic: Algebra · Inequalities. Worth 12 marks.
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Question text
7 A company makes scientific calculators and graphic calculators.
Each day they make x scientific calculators and y graphic calculators.
These inequalities describe the number of scientific and graphic calculators they make each day.
x 1 180 y G 90 x+y G 240
(a) Complete these two statements.
The company makes fewer than ...................... scientific calculators each day .
The company can make a maximum of ...................... calculators each day . [2]
(b) Scientific calculators cost $12 to make.
Graphic calculators cost $18 to make.
Each day the company spends at least $2700 making cal culators.
Show that 2x+3y H 450.
[1]
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© UCLES 2024 (cid:300)(cid:228)(cid:186)(cid:244)(cid:215)(cid:285)(cid:271)(cid:293)(cid:219)(cid:243)(cid:253)(cid:223)(cid:289)(cid:182)(cid:193)(cid:188)(cid:295)(cid:258) 0580/41/O/N/24
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13
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(c) The region R satisfies these four inequalities.
x 1 180 y G 90 x+y G 240 2x+3y H 450
By drawing four suitable lines and shading unwanted regions, find and label the region R.
y
250
200
150
100
50
0 x
50 100 150 200 250
[7]
(d) Scientific calculators are sold for a profit of $10.
Graphic calculators are sold for a profit of $30.
Calculate the maximum profit made by the company in one day.
$ ................................................. [2]
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© UCLES 2024 (cid:300)(cid:228)(cid:185)(cid:243)(cid:207)(cid:299)(cid:275)(cid:277)(cid:222)(cid:261)(cid:244)(cid:298)(cid:181)(cid:190)(cid:277)(cid:188)(cid:279)(cid:258) 0580/41/O/N/24
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TON
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* 0000800000014 *
14
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NIGRAM
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