To solve this problem, let's go through each part step-by-step:

Let $I$ represent Akwasi's monthly income.

Part (a): Total fraction spent on rent, food, and clothes

The fractions spent are as follows:

• Rent: $\frac{1}{3}$
• Food: $\frac{1}{4}$
• Clothes: $\frac{1}{5}$

The total fraction spent is the sum of these fractions: $\frac{1}{3} + \frac{1}{4} + \frac{1}{5}$

To add these, we need a common denominator. The least common multiple of 3, 4, and 5 is 60.

$\frac{1}{3} = \frac{20}{60}, \quad \frac{1}{4} = \frac{15}{60}, \quad \frac{1}{5} = \frac{12}{60}$

Now add them: $\frac{20}{60} + \frac{15}{60} + \frac{12}{60} = \frac{47}{60}$

So, the total fraction spent is $\frac{47}{60}$.

Part (b): Fraction left

The total income is represented by 1 (whole), so the fraction left after spending $\frac{47}{60}$ is: $1 - \frac{47}{60} = \frac{60 - 47}{60} = \frac{13}{60}$

Part (c): Monthly income

We know that after spending, Akwasi is left with GH₵390.00, which corresponds to $\frac{13}{60}$ of his monthly income.

Let $I$ be the monthly income. Then: $\frac{13}{60} \times I = 390$

To find $I$, solve for $I$ by dividing both sides by $\frac{13}{60}$: $I = 390 \times \frac{60}{13} = 1800$

Summary of Solutions

1. Total fraction spent on rent, food, and clothes: $\frac{47}{60}$
2. Fraction left: $\frac{13}{60}$
3. Monthly income: GH₵1800.00

Would you like further explanation on any part of this solution?

Related Questions

1. How would the solution change if the amount left was GH₵500?
2. What if Akwasi spent $\frac{1}{3}$ on rent, $\frac{1}{4}$ on food, and $\frac{1}{6}$ on clothes?
3. How would you solve this if given only the total spent instead of fractions?
4. What is the impact on savings if each fraction were increased by $\frac{1}{10}$?
5. Can you generalize a formula for calculating income if the fractions and remaining amount vary?

Tip: When working with fractions, finding a common denominator simplifies addition and subtraction tasks.