Question

I need you to give me the result of the following exercise There are two two-liter bottles, one with a liter of wine and the other with a liter of water. Transfer 1/2 of the contents of the water bottle to the wine bottle and mix thoroughly. The mixture from the wine bottle is then returned to the water bottle, so that the two bottles again have 1 liter of liquid each. In which of the two bottles was more water left? How much wine was left in the water bottle?

60

likes
301 views

Answer to a math question I need you to give me the result of the following exercise There are two two-liter bottles, one with a liter of wine and the other with a liter of water. Transfer 1/2 of the contents of the water bottle to the wine bottle and mix thoroughly. The mixture from the wine bottle is then returned to the water bottle, so that the two bottles again have 1 liter of liquid each. In which of the two bottles was more water left? How much wine was left in the water bottle?

Expert avatar
Nash
4.9
87 Answers
This is a classic problem of liquid transfer between two containers. Initially, we have 1 liter of wine in one bottle and 1 liter of water in the other bottle.

Step 1: Transfer 1/2 liter of water to the wine bottle.
Wine bottle: 1 liter of wine + 0.5 liters of water
Water bottle: 0.5 liters of water

Step 2: Mix thoroughly.
The wine bottle now contains a mixture that is 1/3 water and 2/3 wine.

Step 3: Transfer 1/2 liter of the mixture back to the water bottle.
Water transferred in: 1/3 * 0.5 = 1/6 liters
Wine transferred in: 2/3 * 0.5 = 1/3 liters

Final contents in the wine bottle:
- Wine: 2/3 liters
- Water: 1/3 liters

Final contents in the water bottle:
- Water: 0.5 + 1/6 = 2/3 liters
- Wine: 1/3 liters

More water is left in the: water bottle (2/3 liters)

Amount of wine left in the: water bottle (1/3 liters)

Therefore, both bottles end up with equal amounts of 'foreign' liquid.

{Answer:} The water bottle has more water left, 2/3 liters of water, and there is 1/3 liters of wine in the water bottle.

Frequently asked questions (FAQs)
What fraction of a pizza remains if 3/4 is eaten?
+
Question: What is the limit of (3x^2 - 2x + 1) as x approaches 2?
+
Math question: Find the positive integers that satisfy Fermat’s Last Theorem equation x^n + y^n = z^n for n ≥ 3.
+
New questions in Mathematics
If you have a bag with 18 white balls and 2 black balls. What is the probability of drawing a white ball? And extracting a black one?
Determine all solutions to the inequality |2x + 6| − |x + 1| < 6. Write your final answer in interval notation
90 divided by 40
How do you think the company has increased or decreased its income?
Consider numbers from 1 to 2023. We delete 3 consecutive numbers so, that the avarage of the left numbers is a whole number
Perpetual annuities are a series of payments whose duration has no end. Explain how can we calculate them, if they have no end?
4x/2+5x-3/6=7/8-1/4-x
Log5 625
It is known that the content of milk that is actually in a bag distributes normally with an average of 900 grams and variance 25 square grams. Suppose that the cost in pesos of a bag of milk is given by 𝐶(𝑥) = { 3800 𝑠𝑖 𝑥 ≤ 890 4500 𝑠𝑖 𝑥 > 890 Find the expected cost.
How many square feet of floor area are there in three two-storey apartment houses, each of which is 38 feet wide and 76 feet long?
Given (3x+2)E [2;14] how much money (in soles) does Sophia have if numerically it is the greatest value of x?
The maximum gauge pressure of a hydraulic ramp is 16 atm, with a support area whose diameter is 20 cm. What is the mass of the heaviest vehicle that can be lifted?
Use a pattern approach to explain why (-2)(-3)=6
-1%2F2x-4%3D18
(a) List the set of possible rational zeros of the polynomial function F(x) = 2x3 - 11x2 + 13x - 4. (b) Find all rational zeros of F(x). Only do part B
The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion is greater than 35%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is z= 2.6. Find the P-value for this test.
48 kg of 30% sulfuric acid in a mixture of 10% and 40% sulfuric acid arose. How many kilograms were each of the original solutions?
Identify the slope and y intercept y=11+2/3x
How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7
Slope (7,3) and (9,5)