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Determine the values of A & B

Mathematics

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3 parts
2.1

R350\text{R}350

2.2

E(x)=350+4xE(x) = 350 + 4x

2.3

A=600A = 600

B=410B = 410

Step-by-step solution

5 steps

Part 2.1· 1 step

  1. Identify John's fixed expenses.

    Fixed expenses are costs that do not change with the number of cars washed.

    • Power washer rental: R300 per day
    • Payment to brother Tommy: R50 per day
    Fixed expenses=R300+R50=R350\text{Fixed expenses} = \text{R}300 + \text{R}50 = \text{R}350

    John's fixed expenses per day are R350\boxed{\text{R}350}.

Part 2.2

E(x)=350+4xE(x) = 350 + 4x

  1. Identify the components of total expenses.

    Total expenses consist of fixed expenses and variable expenses.

    • Fixed expenses: R350 (from 2.1)
    • Variable expenses: R4 per car Let xx be the number of cars washed.
  2. Write the formula for total expenses.

    Expenses=Fixed expenses+(Variable cost per car×Number of cars)\text{Expenses} = \text{Fixed expenses} + (\text{Variable cost per car} \times \text{Number of cars}) E(x)=350+4xE(x) = 350 + 4x

    The formula for expenses is E(x)=350+4x\boxed{E(x) = 350 + 4x}.

Part 2.3

A=600A = 600

  1. Determine the value of A.

    A represents the income for 5 cars. John charges R120 per car.

    A=5 cars×R120/car=R600A = 5 \text{ cars} \times \text{R}120/\text{car} = \text{R}600
  2. Determine the value of B.

    B represents the expenses for 15 cars. Use the formula E(x)=350+4xE(x) = 350 + 4x from 2.2.

    B=E(15)=350+4(15)B = E(15) = 350 + 4(15) B=350+60B = 350 + 60 B=410B = 410

    The values are A=600\boxed{A = 600} and B=410\boxed{B = 410}.

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