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What is angle for rent? Calculate the amount Mr. Brown put in living account? x What fraction of his income was rent?

Mathematics

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3 parts
i

40∘\text{40}^\circ

ii

Gh¢1,260.00\text{Gh¢1,260.00}

iii

19\frac{1}{9}

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Part 2

Part i

40∘\text{40}^\circ

What is the angle for rent?

  1. The sum of angles in a pie chart is 360∘360^\circ.

    Add the given angles and subtract from 360∘360^\circ to find the angle for rent (xx).

    x∘+105∘+36∘+30∘+84∘+65∘=360∘x^\circ + 105^\circ + 36^\circ + 30^\circ + 84^\circ + 65^\circ = 360^\circ x∘+320∘=360∘x^\circ + 320^\circ = 360^\circ x∘=360∘−320∘x^\circ = 360^\circ - 320^\circ x∘=40∘x^\circ = 40^\circ

    The angle for rent is 40∘\boxed{\text{40}^\circ}.

Part ii

Gh¢1,260.00\text{Gh¢1,260.00}

Calculate the amount Mr. Brown put in his saving account.

  1. The total monthly income is Gh¢5,400.00.

    The angle for savings is 84∘84^\circ.

  2. Calculate the amount saved using the proportion of the angle.

    Amount saved=Savings angleTotal angle×Total income\text{Amount saved} = \frac{\text{Savings angle}}{\text{Total angle}} \times \text{Total income} Amount saved=84∘360∘×Gh¢5,400.00\text{Amount saved} = \frac{84^\circ}{360^\circ} \times \text{Gh¢}5,400.00 Amount saved=0.2333...×Gh¢5,400.00\text{Amount saved} = 0.2333... \times \text{Gh¢}5,400.00 Amount saved=Gh¢1,260.00\text{Amount saved} = \text{Gh¢}1,260.00

    Mr. Brown put Gh¢1,260.00\boxed{\text{Gh¢1,260.00}} in his saving account.

Part iii

19\frac{1}{9}

What fraction of his income was spent on rent?

  1. The angle for rent is 40∘40^\circ (from part i).

  2. Express this angle as a fraction of the total angle in a circle.

    Fraction on rent=Rent angleTotal angle\text{Fraction on rent} = \frac{\text{Rent angle}}{\text{Total angle}} Fraction on rent=40∘360∘\text{Fraction on rent} = \frac{40^\circ}{360^\circ} Fraction on rent=19\text{Fraction on rent} = \frac{1}{9}

    The fraction of his income spent on rent is 19\boxed{\frac{1}{9}}.

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