Forming Equations: WJEC GCSE Higher June 2019 Unit 2 Q7

Higher June 2019 Unit 2 Q7

WJECHigherCurrent spec5 marksForming Equations Simultaneous Equations

7. 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 (£\(y\)) = £ ……………

Mark scheme

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 2^nd variable.	m1	F.T. their ‘1^st 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.