The following table shows the charges for making an overseas call to Australia.

  1. (a)

    Mrs Jamus paid 32foraphonecalltohersisterinAustralia.Whatwasthedurationofthecall?Leaveyouranswerintermsof32 for a phone call to her sister in Australia. What was the duration of the call? Leave your answer in terms of p$.

    Answer: (a) ___

  2. (b)

    Given that p=60p = 60, find the duration of the call Mrs Jamus made.

    Answer: (b) ___

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Worked solution

10(a)

1. Calculate the amount paid for the additional minutes

Total paid = $32\char36{}32
Charge for first 15 minutes = $2.60\char36{}2.60
Amount paid for additional minutes = $32−$2.60=$29.40\char36{}32 - \char36{}2.60 = \char36{}29.40

2. Convert the additional amount to cents to match the rate unit

Amount in cents = 29.40×100=294029.40 \times 100 = 2940 cents

3. Formulate the expression for the total duration

Additional minutes = 2940p\frac{2940}{p}
Total duration = 15+2940p15 + \frac{2940}{p} minutes

Answer

15+2940p15 + \frac{2940}{p} minutes

10(b)

1. Substitute $p = 60$ into the expression for the duration of the call

From part (a), the duration is 15+2940p15 + \frac{2940}{p}.
Substitute p=60p = 60:
Duration=15+294060\text{Duration} = 15 + \frac{2940}{60}

2. Calculate the final duration

Duration=15+49=64\text{Duration} = 15 + 49 = 64 minutes

Answer

6464 minutes

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