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Numeracy Foundation June 2019 Unit 1 Q8

WJECFoundationCurrent spec14 marksDrawing & Using GraphsGrouped DataRatio & Basic Proportion

8. Aled and Gareth went on holiday to France.

(a) The total cost of the holiday was £660.
  • Aled’s mother paid \(\frac{1}{3}\) of the total cost.
  • Aled and Gareth shared the remaining cost in the ratio 1 : 9.
(i) Calculate how much each person paid towards the cost of the holiday. [4]

Aled’s mother paid £ ……………
Aled paid £ ……………
Gareth paid £ ……………

(ii) Explain how you could use your answers to check that they are correct. [1]
(b) Gareth’s luggage weighed 21·13 kg.
This was over the maximum of 20 kg allowed.

Gareth removed items from his luggage so that its mass was:

  • as close to 20 kg as possible,
  • not greater than 20 kg.

From the following list of items, which two items did Gareth remove?
You must show all your working. [3]

CoatHeadphonesJumperBookHat
820 g300 g320 g340 g200 g
(c) Before going on holiday, Aled made a conversion graph to help him understand prices in euros.
Conversion graph: Pounds from 0 to 60 across, Euros from 0 to 68.40 up (labels 11.40, 22.80, 34.20, 45.60, 57.00, 68.40), straight line from (0, 0) to (60, 68.40)

Use Aled’s conversion graph to answer the following questions.

(i) A camera costs £90.
How much is this in euros? [2]

Camera costs …………… euros

(ii) A meal costs £25.
How much is this in euros? [2]

Meal costs …………… euros

(d) Gareth looked at exchange rates for buying euros.
He recorded the exchange rates for the previous 60 days, as shown below.
£1 = \(b\) eurosFrequency
\(1.00 \leqslant b \lt 1.04\)2
\(1.04 \leqslant b \lt 1.08\)8
\(1.08 \leqslant b \lt 1.12\)16
\(1.12 \leqslant b \lt 1.16\)33
\(1.16 \leqslant b \lt 1.20\)1

Gareth started to draw a frequency diagram to show this information.

Frequency diagram on graph paper: Euros from 1.00 to 1.20 across, Frequency from 0 to 40 up; bars drawn for 1.00–1.04 (height 2), 1.04–1.08 (height 8) and 1.16–1.20 (height 1); the bars for 1.08–1.12 and 1.12–1.16 are missing
(i) Complete the frequency diagram. [1]
(ii) Which is the modal group?
Circle your answer. [1]

60    \(1.08 \leqslant b \lt 1.12\)    33    \(1.12 \leqslant b \lt 1.16\)    16

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