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 is the solution to the inequality 3x + 5 > 10?
+
What is the product of the conjugate of a complex number (3 + 4i) and its absolute value?
+
What is the measure of the third angle in a triangle if the other two angles measure 55Β° and 75Β°?
+
New questions in Mathematics
find the value of the tangent if it is known that the cos@= 1 2 and the sine is negative. must perform procedures.
2+2
1/2x +3 <4x-7
Imagine that you are in an electronics store and you want to calculate the final price of a product after applying a discount. The product you are interested in has an original price of $1000 MN, but, for today, the store offers a 25% discount on all its products. Develop an algorithm that allows you to calculate the final price you will pay, but first point out the elements.
Determine the equations of the recipes that pass through the following pairs of points P1 (2;-1) and p2 (4;-1)
Suppose 56% of politicians are lawyers if a random sample of size 873 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 55% round your answer to four decimal places
To make brine, JosΓ© buys 1 kg of salt and pays 12 pesos. If he buys 4 kg, they charge him 48 pesos, but for 100 pesos they sell him 9 kg. What is the constant of proportionality?
In a store, a person carries 14 kilos of rice and 28 kilos of flour. In what ratio are the kilos found? (Remember to simplify until you reach an irreducible fraction)
If you randomly selected one person from the 900 subjects in this study, what is the probability that the person exhibits the minimum BMI?
A test has 5 multiple choice questions. Each question has 4 alternatives, only one of which is correct. A student who did not study for the test randomly chooses one alternative for each question.(a) What is the probability of him getting a zero on the test?(b) What is the probability of him getting a three or more? The maximum mark for the test is 5, with each question worth one point.
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
Log5 625
If X1 and X2 are independent standard normal variables, find P(X1^2 + X2^2 > 2.41)
Find the center coordinates and radius of a circle for an equation written as: 3x2 + 3y2 - 6y = β€”12Γ— + 24
cube root of 56
2X+2=8
Farm Grown, Inc., produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any not sold by the end of the day, they are sold to a large food processing company for $3 a case. The probability that daily demand will be 100 cases is 0.30, the probability that daily demand will be 200 cases is 0.40, and the probability that daily demand will be 300 cases is 0.30. Farm Grown has a policy of always satisfying customer demands. If its own supply of cases is less than the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is $16 per case. (a) Draw a decision table for this problem (b) What do you recommend?
The following incoming payments show up at a tax inspection: 25 000€ on 19.01.2008, 140 000€ on 27.03.2008 and 19 000€ on a date that which is illegible, and 60 000€ on 15.06.2008. On which date did the payment of the 19 000€ appear, if on 30.06.2008 the money on the account (incl. interest at 4%) is 246 088.89€? Use simple interest and 30E/360 DCC. Solution: 45 days, 15.05.08
Mark is gluing a ribbon around the sides of a picture frame. The frame is 11 inches long and 7 includes wide. How much ribbon does Mark need?
Find the number of liters of water needed to reduce 9 liters of lotion. shave containing 50% alcohol to a lotion containing 30% alcohol.