MathMaster logo

MathMaster

  1. Home
  2. general
  3. 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 th
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 are the key features of a hyperbola defined by the equation (x^2 / a^2) - (y^2 / b^2) = 1? (
+
Question: What is the equation of the logarithmic function \(f(x)\) whose graph passes through the points \((2, 10)\) and \((5, 50)\)? (
+
What is the product and sum of two numbers x and y, given that x = 5 and y = 8? [
+
New questions in Mathematics
If we have the sequence: 3, 6, 12, 24 Please determine the 14th term.
For a temperature range between 177 degrees Celsius to 213 degrees Celsius, what is the temperature range in degrees Fahrenheit.
Given that y = ×(2x + 1)*, show that dy = (2x + 1)" (Ax + B) dx where n, A and B are constants to be found.
7273736363-8
An electrical company manufactures batteries that have a duration that is distributed approximately normally, with a mean of 700 hours and a standard deviation of 40 hours. Find the probability that a randomly selected battery has an average life of less than 810 hours.
Director of reservations believes that 9% of the ticketed passengers are no-shows. If the directors right what is the probability that the proportion of no-shows in a sample of 789 ticketed passengers with differ from the population proportion buy more than 3% round your answer to four decimal places.
Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places
Find the sum of the first 41 terms of the progression that begins: 32, 24, 16, …
Find the derivatives for y=X+1/X-1
Suppose the Golf ball market is perfectly competitive and the functions are known: Q = 120 – 2Px – 2Py 0.2I Q = 2Px 40 Where I = Consumers' income ($200) and Py = Price of Good Y (40) Calculate the equilibrium elasticity: a) 1.6 b) -6 c) 6 d) 0.6
Two business partners have a bank balance of $17,942.00. After the first year their interest brings their balance to $18,928.91. What rate of interest is earned?
P(Z<z)=0.1003
The probability of growing a seedling from a seed is 0.62. How many seeds do I need to plant so that the probability of growing at least one seedling is greater than or equal to 0.87?
We plan to test whether the mean mRNA expression level differs between two strains of yeast, for each of 8,000 genes. We will measure the expression levels of each gene, in n samples of strain 1 and m samples of strain 2. We plan to compute a P-value for each gene, using an unpaired two-sample t-test for each gene (the particular type of test does not matter). a) What are the null hypotheses in these tests (in words)? [2] b) If, in fact, the two strains are identical, how many of these tests do we expect to produce a P-value exceeding 1/4? [2]
You buy a $475,000 house and put 15% down. If you take a 20 year amortization and the rate is 2.34%, what would the monthly payment be?
Let G be the center of gravity of triangle ABC. We draw through A a parallel to BC on which we take a point D so that DG⊥BG. If the area of the quadrilateral AGBD is equal to s, show that AC·BD≥2·s.
Write the inequality in the form of a<x<b. |x| < c^2
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
2.3 X 0.8
To apply a diagnostic test, in how many ways can 14 students be chosen out of 25? if the order does not matter

You might be interested in