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?
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.
Let's assume Mr. Ahmad's monthly salary to be "x".
Mr. Ahmad saved 1/3 of his salary, which is (1/3)x.
He used 1/5 of his monthly salary to buy a mobile phone, which is (1/5)x.
The remainder after saving and buying the phone can be calculated as follows:
Remainder = x - (1/3)x - (1/5)x
To simplify the equation, let's find a common denominator for 3 and 5:
Common denominator = 3 x 5 = 15
Now, convert the fractions to have the same denominator:
Remainder = (15/15)x - (5/15)x - (3/15)x
Remainder = (15 - 5 - 3)/15x
Remainder = (7/15)x
He spent 3/8 of the remainder on transport, which is (3/8) * (7/15)x.
The remaining amount spent on food after purchasing the phone and transportation can be calculated as follows:
Remainder after transportation = (7/15)x - (3/8) * (7/15)x
Let's simplify the equation:
Remainder after transportation = (7/15)x - (3/8) * (7/15)x
Remainder after transportation = (7/15)x - (3/8) * (7/15)x
Remainder after transportation = (7/15)x - (3/8) * (7/15)x
Remainder after transportation = (7/15)x - (21/120)x
Remainder after transportation = (7/15)x - (7/40)x
Remainder after transportation = (40/40)(7/15)x - (15/15)(7/40)x
Remainder after transportation = (280/600)x - (105/600)x
Remainder after transportation = (280 - 105)/600x
Remainder after transportation = 175/600x
The remaining amount, which is $1750, is spent on food. Therefore,
175/600x = 1750
To find x, we rearrange the equation:
x = (1750 * 600) / 175
x = 6000
Now that we found x, we can calculate the actual amount spent on food:
Amount spent on food = (175/600) * (6000)
Amount spent on food = 3500
Therefore, Mr. Ahmad spent $3500 on food.
To find the fraction of his monthly salary spent on food, we need to compare the amount spent on food to his monthly salary.
Fraction spent on food = Amount spent on food / Monthly salary
Fraction spent on food = 3500 / 6000
The fraction spent on food is 35/60, which can be simplified to 7/12.
Therefore, Mr. Ahmad spent 7/12 of his monthly salary on food in May.