Mathematics 0580 · IGCSE · Inequalities

Inequalities — practice question

A car hire firm owns $x$ small cars and $y$ large cars. Altogether, the firm has at least 6 cars. The number of large cars is no more than the number of small cars. The greatest possible number of small cars is 8.
(a)[3]

Give three inequalities, using $x$ and/or $y$, that represent this information.

(b)[1]

A small car can take 4 people and a large car can take 6 people. On one day, no more than 60 people can be carried in total. Show that $2x + 3y \leq 30$.

(c)[6]

Use shading to remove the unwanted parts of the grid, then show and label the region $R$ that meets all four inequalities.

(d(i))[1]

Determine the number of small cars and the number of large cars required to carry exactly 60 people.

(d(ii))[2]

If the company has 7 cars, find the maximum number of people that can be carried.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: $x+y>6$

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