The school canteen is choosing between two water suppliers. The table shows the delivery fee and the price per bottle charged by each. Supplier Delivery fee...
Question 1 Report
The school canteen is choosing between two water suppliers. The table shows the delivery fee and the price per bottle charged by each.
| Supplier | Delivery fee | Price per bottle |
|---|---|---|
| A | £9 | 40p |
| B | £15 | 25p |
- Write an expression, in pence, for the total cost of ordering \(b\) bottles from Supplier A. (1)
- Write an expression, in pence, for the total cost of ordering \(b\) bottles from Supplier B. (1)
- Form an equation to find the number of bottles at which both suppliers charge the same total, and solve it. (3)
- The canteen orders 60 bottles. State, with a reason, which supplier is cheaper for this order. (2)
Answer Details
This question builds two linear cost expressions in pence from a table of delivery fees and unit prices, finds where they are equal, and compares them at a given order size.
Supplier A charges a \(£9 = 900\) pence delivery fee plus \(40\) pence per bottle:
\[900 + 40b\][1 mark]
Supplier B charges a \(£15 = 1500\) pence delivery fee plus \(25\) pence per bottle:
\[1500 + 25b\][1 mark]
Setting the two costs equal:
\[900 + 40b = 1500 + 25b\]Subtracting \(25b\) and subtracting \(900\) from both sides:
\[15b = 600\]Dividing by \(15\):
\[b = 40\][3 marks]
At \(b=60\) bottles: Supplier A costs \(900+40(60)=3300\) pence, and Supplier B costs \(1500+25(60)=3000\) pence. Since \(60\) is greater than the crossover point of \(40\) bottles, and Supplier B has the lower per-bottle rate, Supplier B is cheaper for an order of \(60\) bottles [2 marks].
Below \(40\) bottles, Supplier A's lower delivery fee makes it cheaper overall, but its higher per-bottle price means Supplier B overtakes it as the cheaper option once the order size passes \(40\) bottles.
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