The pie chart below shows the annual salary by Mr. and Mrs. Ats from a joint account.
If $15 \%$ of the salary was spent on rent:
1. What percentage was spent on food?
$\text { Food } =\frac{108^{\circ}}{360^{\circ}} \times 100=\frac{1080}{36}=30=3$
$\therefore 30 \%$ was spent on ford
2. What percentage was spent on clothes
Answer (1)
Calculate the percentage spent on food: 36 0 ∘ 10 8 ∘ × 100 = 30% .
Calculate the angle corresponding to rent: 15% × 36 0 ∘ = 5 4 ∘ .
Calculate the angle corresponding to clothes: 36 0 ∘ − 5 4 ∘ − 10 8 ∘ = 19 8 ∘ .
Calculate the percentage spent on clothes: 36 0 ∘ 19 8 ∘ × 100 = 55% . The percentage spent on food is 30% and the percentage spent on clothes is 55% .
Explanation
Understanding the Problem We are given a pie chart representing the annual salary of Mr. and Mrs. Ats. We know that 15% of their salary is spent on rent, and the pie chart shows that the section for food corresponds to an angle of 108 degrees. Our goal is to find the percentage of their salary spent on food and clothes.
Calculating Percentage Spent on Food First, let's calculate the percentage spent on food. The angle corresponding to food is 108 degrees out of a total of 360 degrees in the pie chart. To find the percentage, we divide the food angle by the total angle and multiply by 100: 36 0 ∘ 10 8 ∘ × 100 = 30 So, 30% of their salary is spent on food.
Calculating Percentage Spent on Clothes Next, we need to find the percentage spent on clothes. We know the percentage spent on rent is 15%, which corresponds to an angle. Let's calculate the angle corresponding to rent: 15% × 36 0 ∘ = 100 15 × 36 0 ∘ = 5 4 ∘ Now we know the angles for rent (54 degrees) and food (108 degrees). We can find the angle for clothes by subtracting these angles from the total angle (360 degrees): 36 0 ∘ − 5 4 ∘ − 10 8 ∘ = 19 8 ∘ Now, we can calculate the percentage spent on clothes by dividing the clothes angle by the total angle and multiplying by 100: 36 0 ∘ 19 8 ∘ × 100 = 55 So, 55% of their salary is spent on clothes.
Final Answer Therefore, 30% of the salary was spent on food and 55% was spent on clothes.
Examples
Understanding how a household spends its income can be visualized using pie charts, similar to this problem. For instance, if a family earns $50,000 a year and spends 30% on housing, 20% on food, 15% on transportation, 10% on healthcare, and 25% on other expenses, this distribution can be represented in a pie chart. Analyzing these percentages helps the family understand where their money is going and make informed decisions about budgeting and saving. This type of analysis is crucial for financial planning and achieving financial stability.
