1. 1
   A plumber charges a call-out fee of £45 plus £30 for each hour he works. Let $h$ be the number of hours worked and $C$ be the total charge in pounds.

   (a)

   Which equation correctly models the total charge?

   [1 mark]

   • A$C = 45 + 30h$
   • B$C = 30 + 45h$
   • C$C = 45h + 30$
   • D$C = 75h$

   (b)

   Using the model $C = 45 + 30h$, if a customer is charged $C = 165$, how many hours did the plumber work?

   [1 mark]

   • A3 hours
   • B4 hours
   • C5 hours
   • D6 hours

   (c)

   The plumber will only accept jobs where the total charge does not exceed £285. Which inequality correctly represents the maximum number of whole hours $h$ he can work?

   [1 mark]

   • A$h \leq 7$
   • B$h \leq 9$
   • C$h \geq 8$
   • D$h \leq 8$

   Total for question 1: 3 marks

2. 2
   Adult tickets for the school play cost £$x$ each. Child tickets cost £$(x - 4)$ each. The school sells 5 adult tickets and 3 child tickets for a first performance, receiving a total of £108.

   (a)

   Form an equation in $x$ and solve it to find the price of an adult ticket.

   [2 marks]

   (b)

   Using $x = 15$ from part (a), a child ticket costs £$(x-4)$ = £11. For a second performance the school raises the adult ticket price to £$y$ and again expects to sell 5 adult tickets and 3 child tickets (still £11 each). They need total takings of at least £150.
   
   Form an inequality in $y$ and solve it to find the minimum whole-pound adult ticket price needed.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A gardener is designing a rectangular lawn. The length is $(x+3)$ metres and the width is $x$ metres. The area of the lawn is $40\,\text{m}^2$.

   (a)

   Form a quadratic equation in $x$ and solve it to find the width of the lawn. (The width must be a positive value.)

   [3 marks]

   (b)

   The gardener also wants to add a square patio next to the lawn with side length $(x-2)$ metres, using the value of $x = 5$ found in part (a).
   
   Calculate the area of the patio and show that the total area of the lawn and patio together is $49\,\text{m}^2$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A café sells coffees at £$c$ each and pastries at £$p$ each. On Monday, 4 coffees and 3 pastries cost £14.50 in total. On Tuesday, 2 coffees and 5 pastries cost £13.90 in total.

   (a)

   Form and solve a pair of simultaneous equations to find the price of a coffee and the price of a pastry.

   [4 marks]

   (b)

   On Wednesday, the café increases both prices found in part (a) by 10%.
   
   Calculate the new price of a coffee and the new price of a pastry, giving each answer to the nearest penny.

   [4 marks]

   (c)

   A customer wants to spend no more than £20 buying only coffees and pastries at the new Wednesday prices (£2.42 per coffee, £2.09 per pastry), and wants at least twice as many pastries as coffees. If she buys $x$ coffees and $y$ pastries:
   
   Write down two inequalities to represent these conditions, then find the maximum number of coffees she could buy if she buys exactly 8 pastries.

   [5 marks]

   Total for question 4: 13 marks

End of questions