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 hyperbolic sine of twice the natural logarithm of the cube root of 5?
+
Math question: What is the equation of a circle with a center at (3, -2) and a radius of 5 units? (
+
Question: How does the Fundamental Theorem of Calculus relate the integral and derivative of a function?
+
New questions in Mathematics
Let f(x)=||x|−6|+|15−|x|| . Then f(6)+f(15) is equal to:
Solution of the equation y'' - y' -6y = 0
Simplify the expression sin³(x)+cos³(x), using trigonometric functions
Karina has a plot of 5000 square meters in which she has decided that 60% of it will be used to plant vegetables. Of this part, 12% will be dedicated to planting lettuce. How much surface area of the plot will be used to grow lettuce?
what is 3% of 105?
5) A family with a father, mother and 3 children must sit on five chairs in a row and the only restriction is that the mother must be at one end. In how many different ways can they be seated?
The length and breadth of my rectangular vegetable garden is 12,5m and 7,25m respectively. What is the perimeter of the garden?
The mean temperature for july in H-town 73 degrees fahrenheit. Assuming that the distribution of temperature is normal what would the standart deviation have to be if 5% of the days in july have a temperature of at least 87 degrees?
Subscribers to the FAME magazine revealed the following preferences for three categories: Fashion 30, Athletics 24 and Business 15. Following these frequencies of observation, compute the chi-square test statistic. At the 0.05 level of significance, would you conclude they are similar?
4x + 8y = 5 2x + 4y = 10
Log5 625
sin 30
reduce the expression (7.5x 12)÷0.3
P(Z<z)=0.1003
A teacher has 25 red and yellow counters altogether. She has 4 times as many red counters than yellow counters. How many yellow counters does the teacher have?
List five numbers that belong to the 5 (mod 6) numbers. Alternate phrasing, list five numbers that satisfy equation x = 5 (mod 6)
effectiveness of fiscal and monetary policy under closed and open economies
Solve the following system of equations using substitution. y=-4x- 11. 3x+7y=-2
Find the symmetric point to a point P = (2,-7,10) with respect to a plane containing a point Po = (3, 2, 2) and perpendicular to a vector u = [1, -3, 2].
An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?