21M.1.SL.TZ1.4

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The price of gas at Leon’s gas station is $$ 1.50$ per litre. If a customer buys a minimum of $10$ litres, a discount of $$ 5$ is applied.

This can be modelled by the following function, $L$ , which gives the total cost when buying a minimum of $10$ litres at Leon’s gas station.

$L (x) = 1.50 x - 5, x \geq 10$

where $x$ is the number of litres of gas that a customer buys.

Find the total cost of buying $40$ litres of gas at Leon’s gas station.

[2]

Find $L^{- 1} (70)$ .

[2]

The price of gas at Erica’s gas station is $$ 1.30$ per litre. A customer must buy a minimum of $10$ litres of gas. The total cost at Erica’s gas station is cheaper than Leon’s gas station when $x > k$ .

Find the minimum value of $k$ .

[3]

Markscheme / solution

$L (40) = 1.50 \times 40 - 5$ (M1)

$= $ 55$ A1

[2 marks]

$70 = 1.50 x - 5$ (M1)

$(x =) 50$ litres A1

[2 marks]

$1.30 x$ (A1)

$1.30 x < 1.50 x - 5$ (M1)

Note: Award M1 for a graph showing two intersecting linear functions, provided one function has a $y$ -intercept of $0$ and the other function has a negative $y$ -intercept.

(minimum value of $k =$ ) $25$ A1

Note: Accept $x > 25$ .

[3 marks]

Examiners’ report

[N/A]