After spending 2/5 of her my money on food and 1/6 on cosmetics a woman was left with 1300 how much money did she have originally
Let's say the total amount of money the woman had originally is represented by "x".
The amount spent on food is 2/5 of her original money, so the money spent on food is (2/5)x.
The amount spent on cosmetics is 1/6 of her original money, so the money spent on cosmetics is (1/6)x.
The remaining amount of money the woman has is 1300, so we can write an equation:
x - (2/5)x - (1/6)x = 1300
To solve this equation, we need to find a common denominator for 5 and 6, which is 30. Multiplying the equation by 30, we get:
30x - 12x - 5x = 39000
Combining like terms:
13x = 39000
Dividing both sides by 13:
x = 3000
Therefore, the woman originally had 3000 as her total amount of money.
To find out how much money the woman originally had, we'll need to set up an equation using the given information.
Let's assume the woman originally had x amount of money.
According to the given information, she spent 2/5 of her money on food and 1/6 on cosmetics. That means, she spent (2/5)x on food and (1/6)x on cosmetics.
After spending the money on food and cosmetics, she was left with $1300. So, the equation becomes:
x - (2/5)x - (1/6)x = 1300
To solve this equation, we'll need to find a common denominator for 5 and 6. The least common multiple of 5 and 6 is 30.
So, let's rewrite the equation with a common denominator:
(30/30)x - (12/30)x - (5/30)x = 1300
Now, let's simplify:
(13/30)x = 1300
To solve for x, we can multiply both sides of the equation by 30/13:
x = 1300 * (30/13)
Calculating this, x ≈ 3000.
Therefore, the woman originally had approximately $3000.
Let's assume the original amount of money she had is x.
She spent 2/5 of x on food, so she had (1-2/5)x = 3/5*x left.
She spent 1/6 of the remaining money on cosmetics, so she had (1-1/6)(3/5*x) = 5/6*(3/5*x) = 3/6*x = 1/2*x left.
We are given that she had 1300 left, which is 1/2*x, so we can set up the equation:
1/2*x = 1300.
Multiplying both sides of the equation by 2, we get x = 1300 * 2.
x = 2600.
Therefore, she originally had 2600 dollars.