This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to questions 4 and 5. Question 4: i) Find the value of x. Step 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 = 350 Step 2: Calculate the value of x. The total number of people is the sum of all categories. 400 = 350 + x x = 400 - 350 x = 50 The value of x is 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^. Step 1: Calculate the angle for each category. • Graphic: (150)/(400) × 360^ = 0.375 × 360^ = 135^ • Ghanaian Times: (100)/(400) × 360^ = 0.25 × 360^ = 90^ • Mirror: (75)/(400) × 360^ = 0.1875 × 360^ = 67.5^ • Daily Guide (x=50): (50)/(400) × 360^ = 0.125 × 360^ = 45^ • Free Press: (25)/(400) × 360^ = 0.0625 × 360^ = 22.5^ Step 2: Summarize the angles for drawing the pie chart. The angles for the pie chart sectors are: • Graphic: 135^ • Ghanaian Times: 90^ • Mirror: 67.5^ • Daily Guide: 45^ • Free Press: 22.5^ (You would use these angles to draw the respective sectors in a circle.) Question 5: i) Find angle y representing savings for the month. Step 1: Sum the known angles in the pie chart. The sum of all angles in a circle is 360^. 108^ (Food) + 84^ (Others) + 72^ (Rent) + 60^ (Clothing) = 324^ Step 2: Calculate angle y. y + 324^ = 360^ y = 360^ - 324^ y = 36^ The angle y representing savings is 36^. ii) What's the man's salary for the month? Step 1: 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^. Let S be the total salary. Rent ExpenditureTotal Salary = Angle for Rent360^ (180)/(S) = (72)/(360) Step 2: Solve for the total salary S. S = 180 × (360)/(72) S = 180 × 5 S = 900 The man's salary for the month is Gh¢900.00. iii) By how much does expenditure on others exceed that on clothing. Step 1: Calculate the expenditure on "Others". The angle for "Others" is 84^. Expenditure on Others = (84^)/(360^) × Gh¢900 Expenditure on Others = (7)/(30) × 900 Expenditure on Others = 7 × 30 = Gh¢210.00 Step 2: Calculate the expenditure on "Clothing". The angle for "Clothing" is 60^. Expenditure on Clothing = (60^)/(360^) × Gh¢900 Expenditure on Clothing = (1)/(6) × 900 Expenditure on Clothing = Gh¢150.00 Step 3: Find the difference. Difference = Expenditure on Others - Expenditure on Clothing Difference = Gh¢210.00 - Gh¢150.00 Difference = Gh¢60.00 The expenditure on others exceeds that on clothing by Gh¢60.00. Send me the next one 📸