Linda spent one fourth of her money on books 1/3 of her money on food and 1/5 of the remainder on her money on drinks if she then had $21.55 left over how much money did you start with?
Let's represent the amount of money Linda had initially as "x".
Linda spent 1/4 * x on books.
She spent 1/3 * x on food.
The remainder after these two expenses is x - 1/4 * x - 1/3 * x = 1 * x - 1/4 * x - 1/3 * x = (12/12) * x - 3/12 * x - 4/12 * x = (5/12) * x.
Linda then spent 1/5 * (5/12 * x) on drinks, which is (1/5) * (5/12 * x) = (1 * x) / (5 * 12) = x/60.
After spending on drinks, Linda had x - x/60 = 59/60 * x left.
The remaining amount is given as $21.55, which can be expressed as (59/60 * x) = $21.55.
Solving for x,
59/60 * x = $21.55,
x = $21.55 * 60 / 59,
x ≈ $21.92.
Therefore, Linda initially had approximately $21.92.
To find out how much money Linda started with, we need to work backwards from the amount she had left over.
Let's assume Linda started with x dollars.
Linda spent 1/4 of her money on books, so she had 3/4 of her money remaining: (3/4)x.
She then spent 1/3 of that remaining money on food, leaving her with 2/3 of (3/4)x: (2/3) * (3/4)x = (2/3)*(3/4)x = (2/4)x = (1/2)x.
Next, Linda spent 1/5 of the remaining money on drinks, leaving her with 4/5 of (1/2)x: (4/5) * (1/2)x = (4/10)x = (2/5)x.
Finally, we know that Linda had $21.55 left over, so:
(2/5)x = $21.55
To solve for x, we can multiply both sides of the equation by the reciprocal of (2/5), which is 5/2:
x = $21.55 * (5/2)
x = $53.875
Therefore, Linda started with $53.875.