Rowan wants to post a number of packages. He has 10 of each of the following stamps.
1 New Zealand dollar ($1) = 100 cents (100c)
Rowan wants to:
put the correct postage on each package,
use as few of his stamps as possible.
Select the stamps he needs to post each of the following packages.
(i) Documents, postage $3.60 [2]
(ii) Birthday present, postage $7.40 [2]
(b)
Rowan is coming to Wales on holiday. The conversion rate at the exchange shop is $1 = £0.53. The exchange shop only has £10 and £20 notes.
Rowan only has $550 saved. He wants to exchange as close to $550 as possible. He asks for as few notes as possible.
Calculate:
how many of each British note Rowan gets,
how much he pays for his currency, correct to the nearest cent.
You must show all your working. [6]
Mark scheme (a)
Scheme
Marks
Comments
(i) ($)1.80 and ($) 1.80
B2
Ignore units stated in £, p in error Accept giving the names of the stamps
B1 for stamps from those available with sum $3.60, but using 3 stamps, i.e.
($)1.60, ($)1.60 and 40(c)
($)2.80, 40(c) and 40(c)
Do not accept with 4 stamps or more
(ii) ($)2.80, ($)2.80 and ($)1.80 or ($)2.30, ($)2.30 and ($)2.80 in any order
B2
Ignore units stated in £, p in error Accept giving the names of the stamps, e.g. 2 Church of Good Shepherd and 1 Mount Taranaki
B1 for stamps from those available with sum $7.40, but using (4 or) 5 stamps, i.e.
($)2.80, ($)2.30, ($)1.80, 40(c), 10(c)
($)2.80, ($)2.30, ($)1.60, 40(c), 30(c)
2 × ($)2.80, ($)1.60, 2 × 10(c)
3 × ($)2.30, 40(c), 10(c)
3 × ($)1.80, ($)1.60, 40(c)
($)2.30, 3 × ($)1.60, 30(c)
($)2.30, ($)1.80, 2 × ($)1.60, 10(c)
Do not accept with 6 stamps or more, e.g. 4 × ($)1.80 and 2 × 10(c)
Mark scheme (b)
Scheme
Marks
Comments
(Change to £) 550 × 0.53
M1
(£)291.5(0)
A1
(Only £10 and £20 notes available so he can buy) (£)290
A1
FT ‘their (£)291.5(0)’ (provided not a multiple of 10) rounded down to nearest multiple of 10 Accept stated or implied as (£)1.50 can’t be converted Sight of (£)290 with no incorrect working implies previous A1
(Fewest number of notes making up £290,) 14 £20 (notes) and 1 £10 (notes)
A1
FT ‘their £290’ provided it is a multiple of 10 Must be fewest number of notes Sight of correct notes with no incorrect working implies previous A1
(Cost in $ to buy £290 is ) 290 ÷ 0.53 or 550 – 1.5(0) ÷ 0.53 (= 550 – 2.83...)
M1
FT ‘their whole number multiple of £10’ ÷ 0.53 Ignore attempt at any further calculation if 290 ÷ 0.53 seen
($)547.17
A1
Must be <($)550 and depends on M1 M1 previously awarded Must be to the nearest cent Mark final answer
If final M0 A0, then award SC1 for ($)2.83 (left) or similar FT
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