Quelpr
3 marksRepresenting Linear Inequalities (One Variable)

CSEC Mathematics · 2022 · Paper 2 · Question 8(a)

A rental company has x cars and y minivans. The company has at least 8 vehicles altogether. The number of minivans is less than or equal to the number of cars. The number of cars is no more than 9.

Write down THREE inequalities, in terms of x and/or y, other than x \ge 0 and y \ge 0, to represent this information.

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Other parts of this question

  1. 8(b)A car can carry 4 people and a minivan can carry 6 people. There are at most 60 persons to be taken on a tour. Show that 2x + 3y \le 30.[1 mark]
  2. 8(c)On the grid below, plot the four lines associated with the inequalities in (a) and (b). Shade and label the region that satisfies ALL four inequalities R.[5 marks]
  3. 8(d)(i)Determine the two combinations for the MINIMUM number of cars and minivans that can be used to carry EXACTLY 60 people on the tour.[2 marks]
  4. 8(d)(ii)The company charges 75 to rent a car and 90 to rent a minivan. Show that the MINIMUM rental cost for this tour is $990.[1 mark]

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