Foundation November 2023 Paper 3 Q14

14 Des delivers takeaways to houses A, B and C.

Scale: 1 cm represents 3 miles

Not drawn accurately

Des drives

from T to A and back

and

from T to B, then B to C, then C to T.

Des is paid

40p for each mile he drives

and

£1.35 for each house he delivers to.

How much is Des paid in total for this work? [4 marks]

Mark scheme

Answer	Mark	Comments
Alternative method 1
\(0.6 + 0.6 + 1.3 + 0.8 + 1.7\) or 5	M1	oe condone one missing or incorrect distance
their \(5 \times 3\) or 15	M1dep
their \(15 \times 0.4(0) + 3 \times 1.35\) or \(6(.00) + 4.05\)	M1dep	oe working in pence their 15 can be a truncated or rounded up decimal
10.05	A1	SC2 6.05
Alternative method 2
\(0.6 \times 3\) or 1.8 or \(1.2 \times 3\) or 3.6 or \(1.3 \times 3\) or 3.9 or \(0.8 \times 3\) or 2.4 or \(1.7 \times 3\) or 5.1	M1
\(0.6 \times 3 + 0.6 \times 3 + 1.3 \times 3 + 0.8 \times 3 + 1.7 \times 3\) or \(1.8 + 1.8 + 3.9 + 2.4 + 5.1\) or 15	M1dep	oe condone one missing or incorrect distance
their \(15 \times 0.4(0) + 3 \times 1.35\) or \(6(.00) + 4.05\)	M1dep	oe working in pence their 15 can be a truncated or rounded up decimal
10.05	A1	SC2 6.05
Alternative method 3
\(0.6 \times 3\) or 1.8 or \(1.2 \times 3\) or 3.6 or \(1.3 \times 3\) or 3.9 or \(0.8 \times 3\) or 2.4 or \(1.7 \times 3\) or 5.1	M1
\(0.6 \times 3 \times 0.4\) or 0.72 or \(1.2 \times 3 \times 0.4\) or 1.44 or \(1.3 \times 3 \times 0.4\) or 1.56 or \(0.8 \times 3 \times 0.4\) or 0.96 or \(1.7 \times 3 \times 0.4\) or 2.04	M1dep	oe working in pence
\(0.6 \times 3 \times 0.4 \times 2 + 1.3 \times 3 \times 0.4 + 0.8 \times 3 \times 0.4 + 1.7 \times 3 \times 0.4 + 3 \times 1.35\) or \(0.72 \times 2 + 1.56 + 0.96 + 2.04 + 3 \times 1.35\) or \(6(.00) + 4.05\)	M1dep	oe working in pence condone one missing or incorrect distance
10.05	A1	SC2 6.05

Units must be consistent unless recovered
All correct except for missing the return distance from A eg \(0.6 + 1.3 + 0.8 + 1.7\) or 4.4 \(4.4 \times 3 = 13.2\) \(13.2 \times 0.4 + 3 \times 1.35 = 9.33\)	M1M1M1A0
Example using their 15 truncated or rounded up for each mile \(0.6 + 1.3 + 0.8 + 1.7\) or 4.4 \(4.4 \times 3 = 13.2\) \(13 \times 0.4 + 3 \times 1.35 = 9.25\) or \(14 \times 0.4 + 3 \times 1.35 = 9.65\)	M1M1M1A0
\(3.6 + 3.9 + 5.1\) (BC missing)	M1M1
\(3.9 + 2.4 + 5.1\) without further working (TA and AT missing)	M1M0