Intermediate June 2019 Unit 2 Q15
15. The Morgan family and the Smith family are on holiday in Aberystwyth.
There are 7 adults and 2 children in the Morgan family.
There are 4 adults and 3 children in the Smith family.
Both families visit a Craft Centre.
The entry price to the Craft Centre is £\(x\) for adults and £\(y\) for children.
The total cost for the Morgan family is £41.50.
The total cost for the Smith family is £29.75.
Form two equations in terms of \(x\) and \(y\).
Solve your equations, using an algebraic method, to find the entry price for adults and the entry price for children. [5]
The adult entry price (£\(x\)) = £ …………… The child entry price (£\(y\)) = £ ……………
| Scheme | Marks | Comments |
|---|---|---|
| 7x + 2y = (£)41.5(0) AND 4x + 3y = (£)29.75 | B1 | Allow use of other letters to denote variables. B0 for using 4150 and 2975. |
| Method to eliminate variable (Attempt at equal coefficients and subtraction) | M1 | FT ‘their equations’ if of equal difficulty. Allow 1 error in one term, not one with equal coefficients. |
| First variable found x =(£) 5 or y = (£)3.25. | A1 | C.A.O. (for their equations if FT.) |
| Substitute to find the 2nd variable. | m1 | F.T. their ‘1st variable’. |
| Second variable found. | A1 | FT answers should be given to the nearest penny (rounded or truncated). If M0, award SC2 (with possible B1) for both answers of (£) 5 AND (£)3.25. |