# 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

X= 5000×10÷3

X=16666.67 naira

Thanks

## 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

= 3x/4

3. She spent 1/3 of the remaining salary on food:

Food = 1/3 * Remaining Salary

= 1/3 * (3x/4)

= x/4

4. The remaining salary after spending on rent and food:

Remaining Salary = Remaining Salary - Food

= (3x/4) - (x/4)

= 2x/4

= x/2

5. She spent 2/5 of the rest on transport:

Transport = 2/5 * Remaining Salary

= 2/5 * (x/2)

= x/5

6. The remaining salary after spending on rent, food, and transport:

Remaining Salary = Remaining Salary - Transport

= (x/2) - (x/5)

= (5x/10) - (2x/10)

= 3x/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.