Foundation November 2021 Paper 3 Q26
26 At a country park there is a house, a museum and a garden.
The table shows the prices per person to visit the park.
| Price per person | |
|---|---|
| Garden only | Free |
| House and museum | £12.50 |
| House only | £8 |
| Museum only | £7 |
One day, 480 people visit the park.
67 visit the garden only.
40% visit the house and the museum.
\(\dfrac{3}{8}\) visit the house only.
The rest visit the museum only.
In total, how much do the 480 people pay to visit the park?
You may use the Venn diagram to help you. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(480 \times 0.4\) or 192 | M1 | oe implied by 2400 |
| \(480 \times \dfrac{3}{8}\) or 180 | M1 | oe implied by 1440 |
| \(480 -\) their \(192 -\) their \(180 - 67\) or 41 | M1 | oe implied by 287 |
| their \(192 \times 12.5 +\) their \(180 \times 8 +\) their \(41 \times 7\) or \(2400 + 1440 + 287\) | M1 | |
| 4127 | A1 |
Additional guidance
| Method marks may be awarded for correct work seen on Venn diagram or in working, with no or incorrect answer, even if this is seen amongst multiple attempts | |
| For the 4th method mark, incorrectly placed values from their Venn diagram may be used or values connected to the correct category eg if house only and museum only values transposed on the Venn diagram accept their \(192 \times 12.5 +\) their \(41 \times 8 +\) their \(180 \times 7\) | |
| 40% of 413 = 165, \(\dfrac{3}{8}\) of 165 = 62, \(413 - 62 - 165 = 186\) \(165 \times 12.50 + 62 \times 8 + 186 \times 7 = 3860.50\) | M0M0M1M1A0 |
| H = 154.875, H&M = 165.2 \(480 - 67 - 154.875 - 165.2\) | M0M0M1 |