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A company charges a fixed fee of Sh 50 plus Sh 20 per kilometer. Calculate the total charge C for k kilometers. Then, calculate the percentage commission if the commission received is Sh 30,000 on tot

Mathematics

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Here are the solutions to your problems:

1. a) Company charges:
Let CC be the total charge and kk be the number of kilometers.
The fixed charge is Sh 50.
The charge per kilometer is Sh 20.
The total charge can be expressed as:

C=50+20kC = 50 + 20k

1. b) Percentage commission:

  1. Identify the commission amount and the total sales amount.

    Commission received = Sh 30,000
    Total sales amount = Sh 600,000

  2. Calculate the percentage commission.

    Percentage Commission =CommissionTotal Sales×100%= \frac{\text{Commission}}{\text{Total Sales}} \times 100\%

    Percentage Commission=30000600000×100%\text{Percentage Commission} = \frac{30000}{600000} \times 100\% Percentage Commission=360×100%\text{Percentage Commission} = \frac{3}{60} \times 100\% Percentage Commission=120×100%\text{Percentage Commission} = \frac{1}{20} \times 100\% Percentage Commission=0.05×100%\text{Percentage Commission} = 0.05 \times 100\% Percentage Commission=5%\text{Percentage Commission} = \boxed{\text{5\%}}

    2. Gradient of a line:

  3. Identify the coordinates of the two points.

    Let (x1,y1)=(4,5)(x_1, y_1) = (4, 5) and (x2,y2)=(8,3)(x_2, y_2) = (8, 3).

  4. Use the gradient formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.

    m=3−58−4m = \frac{3 - 5}{8 - 4} m=−24m = \frac{-2}{4} m=−12m = \boxed{-\frac{1}{2}}

    3. Solving simultaneous equations by substitution:
    Given equations:

    1. 2x−y=62x - y = 6
    2. x−y=1x - y = 1
  5. Express xx in terms of yy from Equation 2.

    From (2): x=1+yx = 1 + y (Equation 3)

  6. Substitute Equation 3 into Equation 1.

    2(1+y)−y=62(1 + y) - y = 6 2+2y−y=62 + 2y - y = 6 2+y=62 + y = 6
  7. Solve for yy.

    y=6−2y = 6 - 2 y=4y = 4
  8. Substitute the value of yy back into Equation 3 to find xx.

    x=1+4x = 1 + 4 x=5x = 5

    The solution is x=5,y=4\boxed{x=5, y=4}.

    Solving the inequality:
    Given the inequality: −3<2x−5-3 < 2x - 5

  9. Add 5 to all parts of the inequality.

    −3+5<2x−5+5-3 + 5 < 2x - 5 + 5 2<2x2 < 2x
  10. Divide all parts by 2.

    22<2x2\frac{2}{2} < \frac{2x}{2} 1<x1 < x

    The solution is x>1\boxed{x > 1}.

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