a bottle is 1/4 full of drink. If 500 ml of drink is added to it the bottle is 2/3 full.
How many milliliters does the bottle hold when it's full?
2/3x = 1/4x + 500
Solve for x.
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To find out how many milliliters the bottle holds when it's full, let's break down the problem step by step.
First, we know that the bottle is initially 1/4 (or 25%) full of drink. Let's assign a variable to represent the total capacity of the bottle when it's full, say x.
Given that the bottle is 1/4 full, we can write this information as 1/4 * x = 500 ml. We multiply the fraction by the variable representing the full capacity to find out how much drink is in the bottle initially.
Next, we are told that when 500 ml of drink is added, the bottle becomes 2/3 (or 66.67%) full. We can represent this information as 2/3 * x = 500 ml + 1/4 * x. Here, we add 500 ml to the initial amount to find the new total amount of drink in the bottle.
Now we can solve for x to determine the full capacity of the bottle.
Let's multiply the fractions by their respective denominators to remove the fractions:
1/4 * x = 500 ml * 4
2/3 * x = 500 ml * 3 + 1/4 * x
Simplifying:
x/4 = 2000 ml
4x/3 = 1500 ml + x/4
Let's get rid of the fractions by multiplying every term by their respective denominators:
4x = 8000 ml
16x/3 = 4500 ml + x/4
Combining like terms:
16x/3 - x/4 = 4500 ml
(64x - 3x)/12 = 4500 ml
61x/12 = 4500 ml
Now we can solve for x by multiplying both sides of the equation by 12/61:
x = (12/61) * 4500 ml
x ≈ 885.25 ml
Therefore, the bottle holds approximately 885.25 milliliters when it's full.