A worker's monthly expenses are represented in a pie chart. Rent is $80, which corresponds to 96 degrees. How much did the worker save if saving is 56 degrees?

Here's how to solve the problem using the information from the pie chart:

First, let's identify the angles for each category from the pie chart:

• Rent: $96^\circ$
• Cloth: $43^\circ$
• Shelter: $45^\circ$
• Food: $120^\circ$
• Saving: $56^\circ$ The sum of these angles is $96^\circ + 43^\circ + 45^\circ + 120^\circ + 56^\circ = 360^\circ$, which is the total angle in a circle.

We are given that Rent charges were $80.00.

Step 1: Determine the total salary.
The rent of $80.00 corresponds to an angle of$96^\circ$. We can use this to find the total salary, which corresponds to$360^\circ. $$ \text{Total Salary} = \frac{80.00}{96^\circ} \times 360^\circ $$

$$\text{Total Salary} = \frac{80}{96} \times 360$$ $$\text{Total Salary} = \frac{5}{6} \times 360$$

\text{Total Salary} = 5 \times 60 = $300.00

a) How much did the worker save?

Step 1: Identify the angle for Saving.
From the pie chart, the angle for Saving is $56^\circ$.

Step 2: Calculate the amount saved.
We use the angle for saving and the total salary.

$$\text{Amount saved} = \frac{56^\circ}{360^\circ} \times \text{Total Salary}$$

\text{Amount saved} = \frac{56}{360} \times $300.00

$$\text{Amount saved} = \frac{56 \times 300}{360} = \frac{56 \times 30}{36} = \frac{56 \times 5}{6} = \frac{280}{6} = \frac{140}{3}$$

\text{Amount saved} \approx \boxed{$46.67}

b) What fraction of his salary was spent on Food?

Step 1: Identify the angle for Food.
From the pie chart, the angle for Food is $120^\circ$.

Step 2: Calculate the fraction.
The fraction is the angle for Food divided by the total angle of the circle.

$$\text{Fraction for Food} = \frac{\text{Angle for Food}}{\text{Total Angle}}$$ $$\text{Fraction for Food} = \frac{120^\circ}{360^\circ} = \boxed{\frac{1}{3}}$$

c) How much did he spend on food?

Step 1: Calculate the amount spent on Food.
Using the fraction for Food from part b) and the Total Salary calculated in the initial step:

$$\text{Amount spent on Food} = \text{Fraction for Food} \times \text{Total Salary}$$

\text{Amount spent on Food} = \frac{1}{3} \times $300.00

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