A woman spent 1/4 of her salary on rent. 1/3 of the remaining on food and 2/5 of the rest on transport. If she has 5000 naira left, what is her monthly salary?
she spent (1/4) + (1/3 * 3/4) + (2/5 * 1/2) = 19/30
so, 11/30 x = 5000
Let her salary be x
Then 1/4 of x is salary i.e 1/4x
Then 1/3 of the remainder on food i.e 1/3× (1-1/4) on food =1/3×3/4=1/4
Then the rest is i.e 1-1/4-1/4 or 3/4-1/4=1/2
Then now amount on transport is 2/5×1/2=1/5
If she has 5000 left i.e 1-1/4-1/4-1/5=6/30 i.e 3/10
Then now we can say 3/10x=5000
Cross mulitiplying we get
Fred spent 2/9 of his paycheck on food and ⅓ on rent. He spent ¼ of the remainder on gas. After all that, he had $210 left. How much was his paycheck?
Well, it's a good thing she still has some money left! Let's do some calculations to find out her monthly salary.
If she spent 1/4 of her salary on rent, that means she has 3/4 left.
Then, if she spent 1/3 of the remaining money on food, she has 2/3 of the 3/4 left.
After that, if she spent 2/5 of the remaining money on transport, she has 3/5 of the 2/3 of the 3/4 left.
Now, we know that she has 5000 naira left. So we can set up the equation:
3/5 * 2/3 * 3/4 * salary = 5000
If you solve that equation, she must be earning 7500 naira as her monthly salary. That's a good amount of money, but I hope she remembers to save some for clown insurance!
To find the woman's monthly salary, we will work backwards step by step.
Let's assume her monthly salary is "x" naira.
1. She spent 1/4 of her salary on rent:
Rent = 1/4 * x
2. The remaining salary after paying the rent:
Remaining Salary = x - Rent
= x - (1/4 * x)
= x - x/4
3. She spent 1/3 of the remaining salary on food:
Food = 1/3 * Remaining Salary
= 1/3 * (3x/4)
4. The remaining salary after spending on rent and food:
Remaining Salary = Remaining Salary - Food
= (3x/4) - (x/4)
5. She spent 2/5 of the rest on transport:
Transport = 2/5 * Remaining Salary
= 2/5 * (x/2)
6. The remaining salary after spending on rent, food, and transport:
Remaining Salary = Remaining Salary - Transport
= (x/2) - (x/5)
= (5x/10) - (2x/10)
Given that she has 5000 naira left, we can set up an equation based on the remaining salary:
Remaining Salary = 5000
3x/10 = 5000
To solve for x, we can multiply both sides of the equation by 10/3:
x = 5000 * 10/3
x = 16666.67 naira
Therefore, her monthly salary is approximately 16666.67 naira.