O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2024 · Q57 Marks

Two companies move boxes. Company A charges $0.50 for each box plus a fixed fee of $125. Company B charges only a fixed fee of $350. Find the number of boxes moved when Company A charges the same as Company B.

(a)Two companies move boxes. Company A charges $0.50 for each box plus a fixed fee of $125. Company B charges only a fixed fee of $350. Find the number of boxes moved when Company A charges the same as Company B.[2]
(b)The maximum mass a van can carry is exactly 770kg. The van carries boxes each of mass 4kg, correct to the nearest kilogram. Find the upper bound for the number of boxes this van can carry.[2]
(c)A lorry contains boxes of three sizes S, M and L. The ratio of the number of boxes S : M = 2 : 7. The ratio of the number of boxes S : L = 5 : 4. The lorry contains 72 boxes of size L. Find the total number of boxes in the lorry.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[2] 450
[2] M1 for 0.5x + 125 = 350 or better
[2] 220 nfww
[2] B1 for 3.5 used
[3] 477
[3] B1 for 10k : 35k : 8k or [S =] 90
[3] M1 for [M =] (their 90)/2 × 7 oe or (72/their 8k) (their 10k + their 35k + their 8k) oe

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