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The following table gives a data from a newspaper survey in Kumasi. 400 people were asked to choose anyone of the newspaper they prefer to read. 5. The pie chart below shows how Mr. Brown spent his salary in the month of January, 2010. He spent Gh¢180.00 on rent.

Mathematics

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Here are the solutions to questions 4 and 5.

Question 4:

i) Find the value of xx.

  1. Sum the known number of people.

    The total number of people surveyed is 400. The sum of the people who prefer Graphic, Ghanaian Times, Mirror, and Free Press is:

    150+100+75+25=350150 + 100 + 75 + 25 = 350
  2. Calculate the value of xx.

    The total number of people is the sum of all categories.

    400=350+x400 = 350 + x x=400−350x = 400 - 350 x=50x = 50

    The value of xx is 50 people\boxed{\text{50 people}}.

    ii) Draw a pie chart for the distribution.

    To draw a pie chart, we first need to calculate the angle for each newspaper category. The total angle in a circle is 360∘360^\circ.

  3. Calculate the angle for each category.

    • Graphic: 150400×360∘=0.375×360∘=135∘\frac{150}{400} \times 360^\circ = 0.375 \times 360^\circ = 135^\circ
    • Ghanaian Times: 100400×360∘=0.25×360∘=90∘\frac{100}{400} \times 360^\circ = 0.25 \times 360^\circ = 90^\circ
    • Mirror: 75400×360∘=0.1875×360∘=67.5∘\frac{75}{400} \times 360^\circ = 0.1875 \times 360^\circ = 67.5^\circ
    • Daily Guide (x=50x=50): 50400×360∘=0.125×360∘=45∘\frac{50}{400} \times 360^\circ = 0.125 \times 360^\circ = 45^\circ
    • Free Press: 25400×360∘=0.0625×360∘=22.5∘\frac{25}{400} \times 360^\circ = 0.0625 \times 360^\circ = 22.5^\circ
  4. Summarize the angles for drawing the pie chart.

    The angles for the pie chart sectors are:

    • Graphic: 135∘135^\circ
    • Ghanaian Times: 90∘90^\circ
    • Mirror: 67.5∘67.5^\circ
    • Daily Guide: 45∘45^\circ
    • Free Press: 22.5∘22.5^\circ (You would use these angles to draw the respective sectors in a circle.)

    Question 5:

    i) Find angle yy representing savings for the month.

  5. Sum the known angles in the pie chart.

    The sum of all angles in a circle is 360∘360^\circ.

    108∘(Food)+84∘(Others)+72∘(Rent)+60∘(Clothing)=324∘108^\circ (\text{Food}) + 84^\circ (\text{Others}) + 72^\circ (\text{Rent}) + 60^\circ (\text{Clothing}) = 324^\circ
  6. Calculate angle yy.

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

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

    ii) What's the man's salary for the month?

  7. Determine the proportion of rent expenditure to the total salary.

    We know that Gh¢180.00 was spent on rent, which corresponds to an angle of 72∘72^\circ.
    Let SS be the total salary.

    Rent ExpenditureTotal Salary=Angle for Rent360∘\frac{\text{Rent Expenditure}}{\text{Total Salary}} = \frac{\text{Angle for Rent}}{360^\circ} 180S=72360\frac{180}{S} = \frac{72}{360}
  8. Solve for the total salary SS.

    S=180×36072S = 180 \times \frac{360}{72} S=180×5S = 180 \times 5 S=900S = 900

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

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

  9. Calculate the expenditure on "Others".

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

    Expenditure on Others=84∘360∘×Gh¢900\text{Expenditure on Others} = \frac{84^\circ}{360^\circ} \times \text{Gh¢}900 Expenditure on Others=730×900\text{Expenditure on Others} = \frac{7}{30} \times 900 Expenditure on Others=7×30=Gh¢210.00\text{Expenditure on Others} = 7 \times 30 = \text{Gh¢}210.00
  10. Calculate the expenditure on "Clothing".

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

    Expenditure on Clothing=60∘360∘×Gh¢900\text{Expenditure on Clothing} = \frac{60^\circ}{360^\circ} \times \text{Gh¢}900 Expenditure on Clothing=16×900\text{Expenditure on Clothing} = \frac{1}{6} \times 900 Expenditure on Clothing=Gh¢150.00\text{Expenditure on Clothing} = \text{Gh¢}150.00
  11. Find the difference.

    Difference=Expenditure on Others−Expenditure on Clothing\text{Difference} = \text{Expenditure on Others} - \text{Expenditure on Clothing} Difference=Gh¢210.00−Gh¢150.00\text{Difference} = \text{Gh¢}210.00 - \text{Gh¢}150.00 Difference=Gh¢60.00\text{Difference} = \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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