7. Rosie is printing two different rectangular pictures of her dog. The small picture has a height of 10 cm and a width of 5 cm. The large picture has a height of 40 cm and a width of 15 cm.
(a)
The small picture costs £2 to print. Each 1 cm2 of the small picture costs the same to print as each 1 cm2 of the large picture.
Calculate the cost of printing the large picture. You must show all your working. [6]
(b)
To make a frame, it costs 40p for each centimetre of the total distance around the outside of the picture.
Diagram not drawn to scale
Calculate the cost of making a frame for the small picture. [3]
Cost of making a frame for the small picture is ……………………
Mark scheme (a)
Scheme
Marks
Comments
(Area of the small picture is) 10 × 5 OR (Area of the large picture is) 40 × 15
M1
(Area of the small picture is) 50 (cm2) (Area of the large picture is) 600 (cm2)
A1 A1
May be implied in further working May be implied in further working
(Cost to print large picture is) \(\dfrac{600}{50}\) × 2(.00) OR For a full proportion method calculated correctly or or with working shown, e.g. 50cm2 is (£)2, 100cm2 is 2 × 2 (=£4), 150cm2 is 2 + 2 × 2 and 600cm2 is 4 × (2 + 2 × 2)
M2
May be seen in stages FT ‘their 10 × 5’ and FT ‘their 40 × 15’
M1 for any one of the following:
(Cost to print 1cm2) 2(.00) ÷ 50 or 4(p) or (£)0.04
600 ÷ 50 or (600 ÷ 50 =) 12 or 12 × 50 = 600
‘their cost to print per 1cm2’ × ‘their 40 × 15’
Proportion method that would lead to a correct response, but includes one error, e.g. 50cm2 is (£)2, 100cm2 is (£)4, 150cm2 is without working ‘(£)5’ with 600cm2 is (4×5 = £) 20
FT for ‘their 50’ and ‘their 600’ (including if perimeters or semi-perimeters)
(£)24 or 2400(p)
A1
Only FT from previous M2 If units are given they must be correct
7(a) Alternative method 1
Scheme
Marks
Comments
(To find the number of small pictures to cover area of the large picture) 40 ÷ 10 AND 15 ÷ 5
M1
Allow 40 ÷ 5 AND 15 ÷ 10
4 (up) and 3 (across)
A2
May be shown on a diagram Allow 8 and 1.5 (from 40 ÷ 5 = 8 and 15 ÷ 10= 1.5)
A1 for any one of the 4 possible divisions accurately evaluated
(Cost to print the large picture) 4 × 3 × (£) 2 or equivalent
M2
FT ‘their 4 across and 3 up’ provided 2 different values ≠ 1 Allow 8 × 1.5 × (£)2 M1 for appropriate sight of 4 × 3 or 8 × 1.5 including if embedded in other working
(Cost to print large picture) (£)24 or 2400(p)
A1
FT from M2 only If units are given they must be correct
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