a bottle is 1/4 full of cordial,if 500 ml of cordial is added to it, the bottle is 2/3 full.how many ml does the bottle hold when full
2/3x - 1/4 x = 500
8/12 - 3/12 = 500
5/12 x = 500
x = 1200
To find out how many milliliters the bottle holds when full, we will break down the problem into steps.
Step 1: Determine the amount of cordial in the bottle initially.
The bottle is initially 1/4 full. Let's represent the total capacity of the bottle as "x".
So, the amount of cordial initially is (1/4) * x.
Step 2: Add 500 ml of cordial to the bottle.
After adding 500 ml of cordial, the bottle becomes 2/3 full. This means the amount of cordial in the bottle is now (2/3) * x.
Step 3: Set up an equation based on the information.
From steps 1 and 2, we have the following equation:
(1/4) * x + 500 = (2/3) * x.
Step 4: Solve the equation to find the value of x.
Let's solve the equation:
(1/4) * x + 500 = (2/3) * x.
To get rid of the denominators, we can multiply the equation by 12:
12 * ((1/4) * x + 500) = 12 * ((2/3) * x).
Simplifying, we have:
3x + 6000 = 8x.
Moving the variables to one side and the constants to the other side:
8x - 3x = 6000.
Simplifying further:
5x = 6000.
Dividing both sides by 5:
x = 6000 / 5.
Therefore, the bottle holds 1200 ml when full.