Numeracy Foundation June 2019 Unit 2 Q6
6. Ian owns two shops. One is in Ffordd Owain and the other is in Arthur Avenue.
For each shop, Ian has been presented with the sunglasses sales for last week.
Ffordd Owain daily sunglasses sales for last week
In total, 90 pairs of sunglasses were sold.
Arthur Avenue daily sunglasses sales for last week
(a)
For each shop, what fraction of the sunglasses sold last week was sold on Friday?
Express your answers as fractions in their simplest terms.
(i)
Ffordd Owain: [2]
Fraction, in its simplest terms ……………
(ii)
Arthur Avenue: [2]
Fraction, in its simplest terms ……………
(b) At the Arthur Avenue shop, what percentage of the sunglasses sold last week was sold on Tuesday? [2]
(c) On Saturday, how many more sunglasses were sold in the Ffordd Owain shop than in the Arthur Avenue shop? [5]
| Scheme | Marks | Comments |
|---|---|---|
| (a)(i) \(\dfrac{80 \pm 2}{360}\) or \(\dfrac{20}{90}\) | M1 | Allow use of ‘÷’ for M1 |
| \(\dfrac{2}{9}\) | A1 | FT only when simplifying possible, 78/360 = 13/60 81/360 = 9/40 82/360 = 41/180 |
| (a)(ii) A correct numerator or denominator in any of the following proper fractions: \(\dfrac{3.5}{14.5}\) or \(\dfrac{14}{58}\) or \(\dfrac{7}{29}\) | M1 | Must be in a proper fraction Allow for sight of 3.5 ÷ 14.5 or 14 ÷ 58 or 7 ÷ 29 |
| \(\dfrac{7}{29}\) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| Sight of \(\dfrac{2}{14.5}\) (× 100) or \(\dfrac{8}{58}\) (× 100) | M1 | FT ‘their 14.5’ or ‘their 58’ from (a)(ii) provided ≠ 90 If restarting, allow an error in a convincing sum to ‘their total’ for M1, but A0 |
| 13.79(...%) or 13.8(%) or 14(%) | A1 | Do not accept 13(%) or 13.7(%) (but unsupported this does imply M1) |
| Scheme | Marks | Comments |
|---|---|---|
| (Ffordd Owain) 140(°) ± 2(°) | B1 | May be seen by Saturday on the pie chart |
| \(\dfrac{140 \pm 2}{360}\) × 90 or (140 ± 2) × 90 ÷ 360 or (140 ± 2) ÷ 360/90 | M1 | |
| 35 (pairs) | A1 | May be seen by Saturday on the pie chart Answer must be a whole number. |
| (Arthur Avenue 4 × 4 =) 16 (pairs of sunglasses) | B1 | Accept 16 shown on the pictogram unambiguously for Saturday |
| (Difference) 19 (pairs of sunglasses) | B1 | FT ‘their Ffordd Owain total’ – ‘their Arthur Avenue total’ for Saturday, provided ‘their Ffordd Owain total’ ≠ 90 and ≠ 140 ± 2, and ‘their Arthur Avenue total’ ≠ 4 |