The problem involves a pie chart representing Mr. Asiedu's monthly expenditure. His monthly income is $GH¢1,800. We need to determine: (i) The fraction of his income spent on food. (ii) How much he spends on rent. (iii) The angle representing savings.

1. Problem Description

The problem involves a pie chart representing Mr. Asiedu's monthly expenditure. His monthly income is $GH¢1,

8

0

0. We need to determine:

(i) The fraction of his income spent on food.

(ii) How much he spends on rent.

(iii) The angle representing savings.

2. Solution Steps

(i) Fraction of income spent on food:

The angle for food is $120^\circ$. The total angle in a circle is $360^\circ$. Therefore, the fraction of income spent on food is given by:

$\frac{120}{360} = \frac{1}{3}$

(ii) Amount spent on rent:

The angle for rent is $90^\circ$. Therefore, the fraction of income spent on rent is:

$\frac{90}{360} = \frac{1}{4}$

The amount spent on rent is this fraction of the total income:

$\text{Rent} = \frac{1}{4} \times GH¢1,800$

$\text{Rent} = GH¢450$

(iii) Angle representing savings:

The angles for the different expenditures are given as:

Food: $120^\circ$

Rent: $90^\circ$

Drinks: $60^\circ$

Clothing: $50^\circ$

The sum of all angles in a circle is $360^\circ$. Let $x$ be the angle representing savings.

$x + 120 + 90 + 60 + 50 = 360$

$x + 320 = 360$

$x = 360 - 320$

$x = 40^\circ$

3. Final Answer

(i) The fraction of Mr. Asiedu's income spent on food is $\frac{1}{3}$.

(ii) Mr. Asiedu spends GH¢450 on rent.

(iii) The angle that represents savings is $40^\circ$.