Higher June 2022 Paper 2 Q16

16 Amol owns a sandwich shop.

The shop is open from Monday to Saturday.

In June, Amol sold 3000 sandwiches.

(a) Amol wants to work out the mean number of sandwiches he sold per day in June.

His method is \(\quad 3000 \div 30 = 100\)

Make one criticism of Amol’s method. [1 mark]

(b) Amol received £6660 from selling the 3000 sandwiches in June.

The numbers of sandwiches sold were in the ratio

\[\text{meat} : \text{cheese} : \text{vegan} = 9 : 4 : 7\]

The price of a meat sandwich is £2.39

The price of a cheese sandwich is £1.89

Work out the price of a vegan sandwich. [4 marks]

Mark scheme (a)

Answer	Mark	Comments
Valid criticism of method indicating or implying that 30 is incorrect	B1	eg the shop was open for fewer than 30 days

Valid criticism with non-contradictory statements	B1
Contradictory statements	B0
30 should be 26	B1
The answer is 115 (allow 116 or 115.4 or 115.38…)	B1
30 should be 25	B1
The answer is 120	B1
30 should be 24 (condone)	B1
The answer is 125 (condone)	B1
The answer is more than 100	B1
The shop wasn’t open for 30 days	B1
He didn’t work every day in June	B1
The shop was shut on Sundays	B1
He is open 6 days a week	B1
The shop isn’t open every day	B1
He should divide by 31	B0
He doesn’t work weekends	B0
There aren’t 30 days in June	B0
Not every month has 30 days	B0
30 should be 27	B0
The answer is less than 100	B0

Mark scheme (b)

Answer	Mark	Comments
Alternative method 1
\(3000 \div (9 + 4 + 7)\) or \(3000 \div 20\) or 150	M1	oe implied by 1350 or 600 or 1050 or 358.5(0) or 283.5(0)
\(9 \times 2.39\) or 21.51 or \(4 \times 1.89\) or 7.56 or 29.07	M1	oe may be embedded or implied eg \(9 \times 2.39 \times\) their 150 or \(4 \times 1.89 \times\) their 150 their 150 can be any number 3226.5(0) or 1134 or 4360.5(0) score M1M1
\((6660 - 9 \times 2.39 \times\) their \(150 - 4 \times 1.89 \times\) their \(150) \div (7 \times\) their \(150)\) or \((6660 - 3226.5(0) - 1134) \div 1050\) or \((6660 - 4360.5(0)) \div 1050\) or \(2299.5(0) \div 1050\)	M1dep	oe eg \((6660 - 9 \times 2.39 \times\) their \(150 - 4 \times 1.89 \times\) their \(150) \div (3000 - 9 \times\) their \(150 - 4 \times\) their \(150)\) or \(\dfrac{219}{100}\) dep on M1M1 their 150 must be from 1st M1
2.19	A1
Alternative method 2
\(3000 \div (9 + 4 + 7)\) or \(3000 \div 20\) or 150	M1	oe implied by 1350 or 600 or 1050 or 358.5(0) or 283.5(0)
\(9 \times 2.39\) or 21.51 or \(4 \times 1.89\) or 7.56 or 29.07	M1	oe may be embedded or implied eg \(9 \times 2.39 \times\) their 150 or \(4 \times 1.89 \times\) their 150 their 150 can be any number 3226.5(0) or 1134 or 4360.5(0) score M1M1
\(\left(\dfrac{6660}{\text{their } 150} - 9 \times 2.39 - 4 \times 1.89\right) \div 7\) or \((44.4(0) - 21.51 - 7.56) \div 7\) or \(15.33 \div 7\)	M1dep	oe eg \((44.4(0) - 29.07) \div 7\) or \(\dfrac{219}{100}\) dep on M1M1 their 150 must be from 1st M1
2.19	A1

Up to M1M1 may be awarded for correct work with no, or incorrect answer, even if this is seen amongst multiple attempts