Solved: Olava’s Pizza Company supplies and delivers large cheese pizzas.The total cost to... [IB Mathematics Applications & Interpretation (Math AI)]

Olava’s Pizza Company supplies and delivers large cheese pizzas.The total cost to the customer, C, in Papua New Guinean Kina (PGK), is modelled bythe functionCn=34.50n+8.50 ,n≥2 ,n∈ℤ,where n, is the number of large cheese pizzas ordered. This total cost includes a fixedcost for delivery.

Question

SLPaper 1

Olava’s Pizza Company supplies and delivers large cheese pizzas.

The total cost to the customer, $C$ , in Papua New Guinean Kina ( $PGK$ ), is modelled bythe function

$C (n) = 34.50 n + 8.50, n \geq 2, n \in ℤ,$

where $n$ , is the number of large cheese pizzas ordered. This total cost includes a fixedcost for delivery.

State, in the context of the question,what the value of $34.50$ represents.

[1]

Verified

Solution

the cost of each (large cheese) pizza / a pizza / one pizza / per pizza (A1) (C1)

Note: Award (A0) for “the cost of (large cheese) pizzas”. Do not accept “the minimum cost of a pizza”.

[1 mark]

State, in the context of the question,what the value of $8.50$ represents.

[1]

Verified

Solution

the (fixed) delivery cost (A1) (C1)

[1 mark]

Write down the minimum number of pizzas that can be ordered.

[1]

Verified

Solution

$2$ (A1) (C1)

[1 mark]

Kaelani has $450 PGK$ .

Find the maximum number of large cheese pizzas that Kaelani can order fromOlava’s Pizza Company.

[3]

Verified

Solution

$450 = 34.50 n + 8.50$ (M1)

Note: Award (M1) for equating the cost equation to $450$ (may be stated as an inequality).

$12.8 (12.7971 \dots)$ (A1)

$12$ (A1)(ft) (C3)

Note: The final answer must be an integer.
The final (A1)(ft) is awarded for rounding their answer down to a whole number, provided their unrounded answer is seen.

[3 marks]

Olava’s Pizza Company supplies and delivers large cheese pizzas.The total cost to the customer, C, in Papua New Guinean Kina (PGK), is modelled bythe functionCn=34.50n+8.50 ,n≥2 ,n∈ℤ,where n, is the number of large cheese pizzas ordered. This total cost includes a fixedcost for delivery.

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