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Formulate expressions for the price of milk and the number of packets sold after the price increase, given initial values and rates of change.

Mathematics

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2 parts
a(i)

(50+4n) shillings(50 + 4n) \text{ shillings}

a(ii)

(530−20n) packets(530 - 20n) \text{ packets}

Step-by-step solution

6 steps

Here are the workings for the expressions:

Part a(i)· 3 steps

The price of a packet of milk after the price was increased

  1. Identify the initial price and the rate of increase.

    The initial price of a packet of milk is 50 shillings.
    The price increases by 4 shillings for each time nn.

  2. Calculate the total increase in price.

    The total increase in price is the rate of increase multiplied by nn.

    Total Increase=4×n=4n shillings\text{Total Increase} = 4 \times n = 4n \text{ shillings}

  3. Formulate the expression for the new price.

    The new price is the initial price plus the total increase.

    New Price=Initial Price+Total Increase\text{New Price} = \text{Initial Price} + \text{Total Increase} New Price=50+4n\text{New Price} = 50 + 4n

    The price of a packet of milk after the price was increased is (50+4n) shillings\boxed{(50 + 4n) \text{ shillings}}.

Part a(ii)

(530−20n) packets(530 - 20n) \text{ packets}

The number of packets of milk sold after the price was increased

  1. Identify the initial number of packets sold and the rate of decrease.

    The initial number of packets of milk sold is 530.
    The number of packets sold decreases by 20 for each time nn.

  2. Calculate the total decrease in the number of packets sold.

    The total decrease in packets sold is the rate of decrease multiplied by nn.

    Total Decrease=20×n=20n packets\text{Total Decrease} = 20 \times n = 20n \text{ packets}

  3. Formulate the expression for the new number of packets sold.

    The new number of packets sold is the initial number minus the total decrease.

    New Number of Packets=Initial Number−Total Decrease\text{New Number of Packets} = \text{Initial Number} - \text{Total Decrease} New Number of Packets=530−20n\text{New Number of Packets} = 530 - 20n

    The number of packets of milk sold after the price was increased is (530−20n) packets\boxed{(530 - 20n) \text{ packets}}.

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