Numeracy Foundation November 2016 Unit 2 Q10
10.
| Railcard for 16 to 25 year olds £30 for a year Get \(\boldsymbol{\frac{1}{3}}\) off all your rail travel |
Nerys and Eleri are sisters.
Nerys is 22 years old and Eleri is 27 years old.
The two sisters live in Holyhead.
Their aunt lives in Milford Haven.
They travel by train to visit their aunt 3 times a year.
Nerys buys a 16-25 Railcard to use for these journeys.
They buy single rail tickets for each journey.
The cost of a single rail ticket from Holyhead to Milford Haven is £84.50.
The journey home from Milford Haven also costs £84.50 per ticket.
In a year, how much less does Nerys pay than Eleri for the journeys to Milford Haven and back?
You must show all your working. [5]
He sometimes travels from Rhyl to Llandudno Junction by train.
The cost of a single rail ticket from Rhyl to Llandudno Junction is £7.80.
Nerys advises Cristiano to buy a Railcard.
Cristiano says,
| It is not worth paying £30 for the Railcard. |
How many times in a year would Cristiano have to travel to make it worthwhile for him to buy a Railcard? [3]
| Scheme | Marks | Comments |
|---|---|---|
| Treat use of 0.333, 0.666 or 0.67 as PA-1, do not accept 0.3 or 0.6 as ⅓ or ⅔ respectively (Note ⅓ × 84.50 = 28.1666……) ( ⅔ × 84.50 = 56.333….. ) | ||
| (Eleri pays 6 × £84.50 =) (£)507 | B1 | |
| (Nerys pays) ⅔ × 6 × 84.5(0) | M1 | Or 6 × 84.5(0) − ⅓ × 6 × 84.5(0) FT ⅔ × ‘their 6 × 84.5(0)’ |
| + 30 | m1 | |
| Amount in the range (£) 367.98 to (£)368.04 | A1 | (Reminder: Depends on both the M and the m mark awarded) |
| (Nerys pays £507 – (£367.98 to 368.04) less than Eleri) An answer in the range (£)138.96 to (£)139.02 | B1 | FT provided attempt 6 × £84.50 for Eleri and M1 & m1 awarded for Nerys. (Omitting the cost of the Railcard gives £169, B0) |
Treat single journey considered as MR-1
| Scheme | Marks | Comments |
|---|---|---|
| (Eleri pays 3 × 84.50 =) £253.50 | B1 | |
| (Nerys pays) ⅔×£253.50 | M1 | |
| +30 | m1 | |
| = (£)198.99 to (£)199.02 | A1 | |
| (difference of) (£)54.48 to (£)54.51 | B1 | (depends on attempt 3 × 84.50 and M1, m1) |
AND also similar to the alternative shown below
Alternative looking directly at the saving:
| Scheme | Marks | Comments |
|---|---|---|
| (Nerys saves=) 1/3 × 6 × (£)84.50 | M2 | |
| (£)168.96 to (£)169.02 | A1 | |
| – 30 | m1 | (FT 'their 169' – 30) |
| (=£) 138.96 to (£)139.02 | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| 1/3 × 7(.)80 | M1 | |
| 30 ÷ 2.60 | M1 | FT 'their 1/3 × 7(.)80' incorrectly evaluated Note: Break-even is 11.538 single journeys. |
| He would need to make 12 (single) journeys (or more) or 6 return journeys (or more) | A1 | CAO Allow ‘if he goes (at least) once a month’ |
Alternative:
M1 for any one correct discounted return or single cost
M1 for method for the equivalent of 12 single or 6 returns, full and discounted costs, with sight of considering also the £30
A1 For either 6 return journeys or 12 singles, with no incorrect working seen
| Return, £ | Discounted return, £ | Discounted + cost of rail card, £ |
|---|---|---|
| 15.60 | 10.40 | 40.40 |
| 31.20 | 20.80 | 50.80 |
| 46.80 | 31.20 | 61.20 |
| 62.40 | 41.60 | 71.60 |
| 78.00 | 52.00 | 82.00 |
| 93.60 | 62.40 | 92.40 |