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The pie chart below shows how Mr. Brown spent his salary in the month of January, 2010. He spent GHC180.00 on rent. i. Find angle y representing savings for the month. ii. What is the man's salary for the month? iii. By how much does expenditure on others exceed that on clothing.

Mathematics

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Answers

3 parts
i

36∘\text{36}^\circ

ii

GH¢900.00\text{GH¢}900.00

iii

GH¢60.00\text{GH¢}60.00

Step-by-step solution

7 steps

Part i· 2 steps

Find angle y representing savings for the month.

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

    Add the given angles for Food, Others, Clothing, and Rent.

    108∘+84∘+60∘+72∘=324∘108^\circ + 84^\circ + 60^\circ + 72^\circ = 324^\circ
  2. Subtract this sum from 360∘360^\circ to find the angle yy for savings.

    y=360∘−324∘=36∘y = 360^\circ - 324^\circ = 36^\circ

    The angle representing savings is 36∘\boxed{\text{36}^\circ}.

Part ii

GH¢900.00\text{GH¢}900.00

What is the man's salary for the month?

  1. The problem states that GH¢180.00 was spent on Rent, which corresponds to an angle of 72∘72^\circ.

    Calculate the monetary value per degree.

    Value per degree=GH¢180.0072∘=GH¢2.50/degree\text{Value per degree} = \frac{\text{GH¢}180.00}{72^\circ} = \text{GH¢}2.50/\text{degree}
  2. The total salary corresponds to the full circle, which is 360∘360^\circ.

    Multiply the value per degree by 360∘360^\circ to find the total salary.

    Total Salary=GH¢2.50/degree×360∘=GH¢900.00\text{Total Salary} = \text{GH¢}2.50/\text{degree} \times 360^\circ = \text{GH¢}900.00

    The man's salary for the month is GH¢900.00\boxed{\text{GH¢}900.00}.

Part iii

GH¢60.00\text{GH¢}60.00

By how much does expenditure on others exceed that on clothing.

  1. Calculate the expenditure on "Others".

    The angle for "Others" is 84∘84^\circ.

    Expenditure on Others=84∘×GH¢2.50/degree=GH¢210.00\text{Expenditure on Others} = 84^\circ \times \text{GH¢}2.50/\text{degree} = \text{GH¢}210.00
  2. Calculate the expenditure on "Clothing".

    The angle for "Clothing" is 60∘60^\circ.

    Expenditure on Clothing=60∘×GH¢2.50/degree=GH¢150.00\text{Expenditure on Clothing} = 60^\circ \times \text{GH¢}2.50/\text{degree} = \text{GH¢}150.00
  3. Find the difference between the expenditure on "Others" and "Clothing".

    Difference=GH¢210.00−GH¢150.00=GH¢60.00\text{Difference} = \text{GH¢}210.00 - \text{GH¢}150.00 = \text{GH¢}60.00

    The expenditure on others exceeds that on clothing by GH¢60.00\boxed{\text{GH¢}60.00}.

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