Question

In May, Mr Ahmad saved 1/3 of his salary and used 1/5 of his monthly salary to buy a mobile phone. He spent 3/8 of the remainder on transport and the rest of the $1750 was spent on food. What fraction of his monthly salary in May was spent on food?

Answer 1

Let's start by using fractions to represent the different expenses:

Saving: 1/3 of monthly salary
Mobile phone: 1/5 of monthly salary
Transport: 3/8 of (monthly salary - savings - mobile phone)
Food: the rest of the monthly salary after subtracting savings, mobile phone, and transport expenses.

To simplify the calculations, let's assume Mr Ahmad's monthly salary is $x.

Saving: 1/3 * x = x/3
Mobile phone: 1/5 * x = x/5
Transport: 3/8 * (x - x/3 - x/5) = 9x/40
Simplifying the expression inside the parentheses:
x - x/3 - x/5 = (15x - 5x - 3x)/15 = 7x/15
Now substituting back into the transport formula:
3/8 * (7x/15) = 7x/40

To find the amount spent on food, we need to add up the savings, mobile phone, and transport expenses and subtract that total from the monthly salary:

Total expenses = x/3 + x/5 + 7x/40
Common denominator for the three fractions: 120
Total expenses = (40x + 24x + 21x)/120
Total expenses = 85x/120 = 17x/24

Amount spent on food = Monthly salary - total expenses
Amount spent on food = x - 17x/24 = 7x/24

To answer the question, we want to express the amount spent on food as a fraction of the monthly salary:
Fraction spent on food = (7x/24) / x
Fraction spent on food = 7/24

Therefore, Mr Ahmad spent 7/24 of his monthly salary in May on food.