Foundation November 2018 Paper 1 Q24
24.
(a) 
Use the diagram to solve the simultaneous equations
\[y - x = 3,\]\[x + 2y = 1.\]Give your answers correct to 1 decimal place. [2]
(b)
A theme park sells entrance tickets.
2 adult tickets and 3 child tickets would cost a total of £72.
3 adult tickets and 1 child ticket would cost a total of £66.
A family ticket costs £45 and allows entry for 2 adults and 2 children.
How much cheaper is it to buy a family ticket than it would be to buy 2 adult and 2 child tickets? [5]
| Scheme | Marks | Comments |
|---|---|---|
| \(x\) = –1.6 or –1.7 | B1 | |
| \(y\) = 1.3 or 1.4 | B1 | If no marks then SC1 for a value of \(x\) between –1.6 and –1.7 and a value of \(y\) between 1.3 and 1.4 or for correct values given as coordinates |
| Scheme | Marks | Comments |
|---|---|---|
| \(2a + 3c = 72\) and \(3a + c = 66\) | B1 | May use other letters or words throughout this part |
| Method to eliminate an unknown e.g. equal coefficients and subtraction | M1 | FT their equations provided one is correct and the other is linear in the same pair of unknowns or rearranges one equation and substitutes into the other Allow one error in one term, not in the equated coefficients |
| Finds one unknown | A1 | CAO; \(a = 18\) or \(c = 12\) |
| Finds the other unknown | A1 | FT ‘their \(a\)’ or ‘their \(c\)’ used in one of their equations |
| (£)15(.00) | B1 | FT 2(‘their derived \(a\)’) + 2(‘their derived \(c\)’) – 45 provided 2(‘their derived \(a\)’) + 2(‘their derived \(c\)’) is greater than 45 |
| (7) |
Alternative
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Adult ticket costs £18, child ticket costs £12 found using trials | B4 | |
| (£)15(.00) FT 2(‘their derived \(a\)’) + 2(‘their derived \(c\)’) – 45 provided 2(‘their derived \(a\)’) + 2(‘their derived \(c\)’) is greater than 45 | B1 |