Theory question 110
Variation(a) The cost, C, of feeding some students in a class is partly constant and partly varies as the number of students, n, in the class. For 8 students, the cost is $70.00 and for 10 students the cost is $90.00. Find: (i) an expression for C in terms of n; (ii) the cost of feeding 12 students.
(b) In the diagram. A, B, C and D are points on a circle. AB ∥ DC, AC and BD intersect at X and ∠BDC = 40°. Find: (i) ∠ACD; (ii) ∠AXD
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(a)(i) C = a + bn: a + 8b = 70 and a + 10b = 90 ⇒ b = 10, a = −10, so C = 10n − 10
(ii) C = 10(12) − 10 = $110
(b)(i) ∠ABD = ∠BDC = 40° (alternate angles, AB ∥ DC); ∠ACD = ∠ABD = 40° (angles in the same segment)
(ii) ∠AXD is an exterior angle of triangle XDC: ∠AXD = 40° + 40° = 80°
'Partly constant and partly varies' means C = a + bn.