a) Determine the table of P = 10(x) + 300 20 b) Write down an equation that can be used to calculate the…

Question

a) Determine the table of P = 10(x) + 300 20 b) Write down an equation that can be used to calculate the income c) Identify the independent variable to determine the cost price of the cups of Milo

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Here are the solutions to the questions:

Calculate the value of Q in TABLE 3 (for 1.2.3 and 1.2.1(a))
The formula for the cost price is given as $C = R9.00n + R9.50$ .
From TABLE 3, when the number of cups ( $n$ ) is Q, the cost price ( $C$ ) is R375.
Substitute these values into the formula:
$375 = 9.00Q + 9.50$
Subtract 9.50 from both sides:
$375 - 9.50 = 9.00Q$ $365.50 = 9.00Q$
Divide by 9.00 to solve for Q:
$Q = \frac{365.50}{9.00}$ $Q \approx 40.6111...$
Since Q represents the number of cups, we will provide the calculated decimal value.
Answer 1.2.1 (a)
Assuming "Determine the table of P of TABLE 3" means to complete the table by finding the value of Q.
The completed TABLE 3 is:
Number of cups of Milo (n): 0, 30, 40.61, 50, 100
Cost price (R) (C): 0, 30, 375, 612.50, 1040
The value of Q is approximately 40.61.
Answer 1.2.1 (b)
The equation that can be used to calculate the income ( $I$ ) is the product of the selling price per cup ( $P$ ) and the number of cups sold ( $n$ ).
$I = P \times n$
The selling price per cup ( $P$ ) is not provided in the given information.
Answer 1.2.1 (c)
In TABLE 3, the cost price (C) depends on the number of cups of Milo (n). Therefore, the independent variable is the one that is varied, which is the number of cups of Milo (n).
Answer 1.2.4
To draw a graph representing the cost, we use the given cost formula $C = 9.00n + 9.50$ . We will generate points for $n$ from 0 to 100.
- For $n=0$ : $C = 9.00(0) + 9.50 = 9.50$ . Point: $(0, 9.50)$
- For $n=30$ : $C = 9.00(30) + 9.50 = 270 + 9.50 = 279.50$ . Point: $(30, 279.50)$
- For $n=50$ : $C = 9.00(50) + 9.50 = 450 + 9.50 = 459.50$ . Point: $(50, 459.50)$
- For $n=100$ : $C = 9.00(100) + 9.50 = 900 + 9.50 = 909.50$ . Point: $(100, 909.50)$ The cost graph should be plotted using these points.
Answer 1.2.5 (a)
The break-even point is the point at which the total cost of producing and selling a product equals the total income generated from its sales. At this point, the business makes zero profit and zero loss.
Answer 1.2.5 (b)
To determine the number of cups of Milo at the break-even point, we need to set the total income ( $I$ ) equal to the total cost ( $C$ ).
The cost equation is $C = 9.00n + 9.50$ .
The income equation is $I = P \times n$ , where $P$ is the selling price per cup.
Setting $I = C$ :
$P \times n = 9.00n + 9.50$
To solve for $n$ (the number of cups at the break-even point), the selling price per cup ( $P$ ) is required. This information is not provided in the question.

The value of Q is $\boxed{\text{40.61}}$ .

A) Determine the table of P = 10(x) + 300 20 b) Write down an equation that can be used to calculate the income c) Identify the independent variable to determine the cost price of the cups of Milo

Step-by-step solution

Calculate the value of Q in TABLE 3 (for 1.2.3 and 1.2.1(a))

Answer 1.2.1 (a)

Answer 1.2.1 (b)

Answer 1.2.1 (c)

Answer 1.2.4

Answer 1.2.5 (a)

Answer 1.2.5 (b)

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