The following questions are from a homework assignment: 1. E-sheen was given ₦20000 for her pocket money and spent it as represented on a pie chart. The amounts spent are given as 2X, 3X, 4X, and X. a

here are the solutions to your problems:

** (Left Column - Pie Chart):**
E-sheen was given ₦20000 for her pocket money and spent it as represented on a pie chart. The amounts spent are given as $2X$, $3X$, $4X$, and $X$.

a) Find X

Step 1: Sum the proportions of money spent.
The total amount spent is the sum of the given parts:

$$2X + 3X + 4X + X = 10X$$

Step 2: Equate the total proportion to the total money.
The total pocket money is ₦20000.

$$10X = 20000$$

Step 3: Solve for $X$.

$$X = \frac{20000}{10}$$ $$X = \boxed{\text{₦}2000}$$

b) How much does she spend on each item?

Step 1: Calculate the amount for each proportion using $X = ₦2000$.
For $2X$:

$$2X = 2 \times 2000 = \text{₦}4000$$

For $3X$:

$$3X = 3 \times 2000 = \text{₦}6000$$

For $4X$:

$$4X = 4 \times 2000 = \text{₦}8000$$

For $X$:

$$X = \text{₦}2000$$

She spends: ₦4000, ₦6000, ₦8000, and ₦2000 on each item.

** (Left Column - Exponents):**
Work out $5^3 \times 5^{-5}$.

Step 1: Apply the exponent rule $a^m \times a^n = a^{m+n}$.

$$5^3 \times 5^{-5} = 5^{3 + (-5)}$$ $$5^{3 + (-5)} = 5^{3-5}$$ $$5^{3-5} = 5^{-2}$$

Step 2: Apply the exponent rule $a^{-n} = \frac{1}{a^n}$.

$$5^{-2} = \frac{1}{5^2}$$ $$5^{-2} = \frac{1}{25}$$

The result is $\boxed{\frac{1}{25}}$.

** (Left Column - Percentage/Fraction):**
12.5% of the people in town are traders. What fraction of the people are in town are traders?

Step 1: Convert the percentage to a fraction by dividing by 100.

$$12.5\% = \frac{12.5}{100}$$

Step 2: Eliminate the decimal by multiplying the numerator and denominator by 10.

$$\frac{12.5 \times 10}{100 \times 10} = \frac{125}{1000}$$

Step 3: Simplify the fraction.
Divide both numerator and denominator by their greatest common divisor.

$$\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}$$

The fraction of people who are traders is $\boxed{\frac{1}{8}}$.

** (Left Column - Polygon):**
A regular polygon has one of its interior angles as $144^\circ$.

a) Name the polygon.

Step 1: Find the exterior angle.
The sum of an interior angle and its corresponding exterior angle is $180^\circ$.

$$\text{Exterior Angle} = 180^\circ - \text{Interior Angle}$$ $$\text{Exterior Angle} = 180^\circ - 144^\circ = 36^\circ$$

Step 2: Find the number of sides ($n$).
For any regular polygon, the sum of its exterior angles is $360^\circ$. Therefore, each exterior angle is $\frac{360^\circ}{n}$.

$$36^\circ = \frac{360^\circ}{n}$$ $$n = \frac{360^\circ}{36^\circ}$$ $$n = 10$$

A polygon with 10 sides is a decagon.

b) Find the sum of its interior angles.

Step 1: Use the formula for the sum of interior angles of an $n$-sided polygon: $(n-2) \times 180^\circ$.
For $n=10$:

$$\text{Sum of Interior Angles} = (10-2) \times 180^\circ$$ $$\text{Sum of Interior Angles} = 8 \times 180^\circ$$ $$\text{Sum of Interior Angles} = 1440^\circ$$

The sum of its interior angles is $\boxed{1440^\circ}$.

** (Right Column - Simple Interest):**
A sum of ₦45000 is invested at 12% per annum simple interest. What is the total amount after 4 years?

Step 1: Identify the given values.
Principal ($P$) = ₦45000
Rate ($R$) = 12% = 0.12
Time ($T$) = 4 years

Step 2: Calculate the simple interest ($SI$).

$$SI = P \times R \times T$$ $$SI = 45000 \times 0.12 \times 4$$ $$SI = 45000 \times 0.48$$ $$SI = \text{₦}21600$$

Step 3: Calculate the total amount ($A$).

$$A = P + SI$$ $$A = 45000 + 21600$$ $$A = \text{₦}66600$$

The total amount after 4 years is $\boxed{\text{₦}66600}$.

** (Right Column - Time Zone):**
The time in Accra is 9:00 am. What time is it in Buenos Aires, in the +3 time zone to the west?

Step 1: Determine the time difference.
"3 time zone to the west" means Buenos Aires is 3 hours behind Accra.
Time difference = 3 hours.

Step 2: Calculate the time in Buenos Aires.
Time in Buenos Aires = Time in Accra - Time difference
Time in Buenos Aires = 9:00 am - 3 hours
Time in Buenos Aires = 6:00 am
The time in Buenos Aires is $\boxed{\text{6:00 am}}$. (The "Find the value of K" part of the question is unclear in this context and is not addressed.)

** (Right Column - Fraction Arithmetic):**
Evaluate $\frac{2}{3} - \frac{1}{4} + \frac{3}{5}$.

Step 1: Find the least common multiple (LCM) of the denominators (3, 4, 5).
The LCM of 3, 4, and 5 is $3 \times 4 \times 5 = 60$.

Step 2: Convert each fraction to an equivalent fraction with a denominator of 60.

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