To find out how much money Leah won from the competition, we can work backwards from the information given.
We know that Leah put $250 towards buying a new computer, which was the remaining amount after she spent a third, a fourth, and a sixth of the money on different items.
Let's break it down step-by-step:
1. Leah used a third of the money to buy a meal plan. This means she spent 1/3 of the money on the meal plan.
2. Leah used a fourth of the money to buy textbooks. This means she spent 1/4 of the money on textbooks.
3. Leah used a sixth of the money to buy a parking permit. This means she spent 1/6 of the money on the parking permit.
Now, let's calculate the total amount Leah spent on the meal plan, textbooks, and parking permit:
1/3 + 1/4 + 1/6
To add fractions, we need to find a common denominator. In this case, the least common denominator is 12.
1/3 can be written as 4/12 (multiply numerator and denominator by 4).
1/4 can be written as 3/12 (multiply numerator and denominator by 3).
1/6 can be written as 2/12 (multiply numerator and denominator by 2).
Adding the fractions together, we get:
4/12 + 3/12 + 2/12 = 9/12
Now, let's subtract the fraction spent from 1 (since 1 represents the total amount of money Leah won) to find the fraction of money Leah has left:
1 - 9/12 = 3/12
So, Leah has 3/12 of the money left after buying the meal plan, textbooks, and parking permit.
We know that Leah put $250 towards buying a new computer, which represents 3/12 of the money she won. So, we can set up the following equation:
(3/12) * x = $250
To solve for x, we can multiply both sides of the equation by the reciprocal of 3/12, which is 12/3:
(3/12) * x * (12/3) = $250 * (12/3)
This simplifies to:
x = $250 * 12/3
x = $1,000
Therefore, Leah won $1,000 from the competition.