The Venn diagram shows the number of customers who bought these items.
(i) How many baths did these customers buy? [1]
(ii) A bath costs £180. A set of taps cost £60.
Calculate the total cost of the baths and sets of taps bought by these 80 customers. [3]
(b) HydraDwr also sells pipes and couplings to join the pipes.
(i) 3 pipes are joined together using 2 couplings, as shown below.
Diagram not drawn to scale
How many couplings are needed to join 6 pipes? [1]
(ii) An equation is used to work out the number of couplings needed to join pipes.
\(P\) = the number of pipes \(C\) = the number of couplings
Which of the following equations can be used to calculate the number of couplings needed? Circle your answer. [1]
\(C = 2P\) \(C = P + 1\) \(C = P - 1\) \(C + P = 1\) \(C = P\)
Mark scheme (a)
Scheme
Marks
Comments
(i) 50 (baths)
B1
Do not accept 50/80
(ii) All appropriate products given, i.e.
(Bath, Taps) (10 + 40) × 180 AND (40 + 30) × 60 (=9000 AND 4200)
(Bath, Bath & tap, Tap) 10 × 180 AND 40 × (180 + 60) AND 30 × 60 (=1800 AND 9600 AND 1800)
(Bath, Split bath & tap, Tap) 10 × 180 AND 40×180 AND 40×60 AND 30×60 (= 1800 AND 7200 AND 2400 AND 1800)
M2
FT from either an error in evaluating ‘10 + 40’ or for 40 < ‘their 50’ < 60 in (a)(i) Allow intention if brackets are missing (for M2 or M1) Intention to ‘add’ is not required If additional working is seen, there needs to be clear indication of which are the appropriate products
M1 for any one of the following partial method, ignore any additional inappropriate products:
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