Two jugs are filled with water. If you remove 1 liter of water from the first jug, then the two jugs contain the same amount of water. If you remove 2 liters from the second, then the second jug would contain half as much as the first. How many liters of water are in the largest jug?
Now it's your turn. You've wasted a couple of tutors' time. Now you can show how YOU think you should solve this problem.
The larger jug is six liters before you tske away the one liter
*Take
Let's solve this problem step by step.
First, let's assume that the amount of water in the larger jug is represented by the variable "x" liters.
According to the given information, if you remove 1 liter of water from the first (smaller) jug, the two jugs will contain the same amount of water. This means that the larger jug originally had x + 1 liters of water while the smaller jug had x liters of water.
Next, we are told that if you remove 2 liters from the second (larger) jug, it will contain half as much water as the first jug. So, after removing 2 liters, the second jug will have (x - 2) liters of water, which is equal to half the amount of water in the first jug, i.e., (x + 1)/2.
To solve for x, we can set up the equation:
(x + 1)/2 = x - 2
Now, let's solve this equation step by step:
Step 1: Multiply both sides of the equation by 2 to eliminate the fraction:
(x + 1) = 2(x - 2)
Step 2: Distribute the 2 on the right side:
x + 1 = 2x - 4
Step 3: Subtract x from both sides of the equation:
1 = x - 4
Step 4: Add 4 to both sides of the equation:
5 = x
Therefore, the larger jug originally contained 5 liters of water.
So, the answer is that the largest jug initially contained 5 liters of water.