19N.1.SL.TZ0.T_2

pestleMathematicsAISLPaper 119N· sl-2-5-modelling-functionssource ↗

M-Line is a company that prints and sells custom designs on T-shirts. For each order, they charge an initial design fee and then an additional fee for each printed T-shirt.

M-Line charges $M$ euros per order. This charge is modelled by the linear function $M\left( x \right) = 5x + 40$ , where $x$ is the number of T-shirts in the order.

EnYear is another company that prints and sells T-shirts. The price, $N$ euros, that they charge for an order can be modelled by the linear function $N\left( x \right) = 9x$ , where $x$ is the number of T-shirts in the order.

Write down the initial design fee charged for each order.

[1]

Find the total amount charged for an order of $94$ T-shirts.

[2]

Write down the number of T-shirts in an order for which EnYear charged $63$ euros.

[1]

An order of $p$ T-shirts will be charged the same price by both M-Line and EnYear.

Find the value of $p$ .

[2]

Markscheme / solution

$40$ (euros) (A1) (C1)

[1 mark]

$\left( {M\left( {94} \right) = } \right)5\left( {94} \right) + 40$ (M1)

Note: Award (M1) for correct substitution of $94$ into given function.

$510$ (euros) (A1) (C2)

[2 marks]

$7$ (T-shirts) (A1) (C1)

[1 mark]

$9p = 5p + 40$ (M1)

Note: Award (M1) for equating the given functions. Accept a sketch showing both functions.

$\left( {p = } \right)\,\,10$ (T-shirts) (A1) (C2)

[2 marks]

Examiners’ report

[N/A]