A mixture of 125 gallons of wine and water contains 20% water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?a)10 galsb)8.5 galsc)8 galsd)8.33 galsCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

20% of 125 is 25.....i.e 100 wine and 25 water.....now 25+x=25%(125+x)..........so x=8.33 ans

Answer

Given:
- A mixture of 125 gallons of wine and water
- The mixture contains 20% water
- We need to increase the percentage of water to 25% of the new mixture

To solve the problem, we can use the following steps:

1. Determine the amount of water in the original mixture:
- 20% of 125 gallons = 0.2 x 125 = 25 gallons of water
- Therefore, the original mixture contains 125 - 25 = 100 gallons of wine

2. Let's assume that x gallons of water must be added to the mixture to achieve the desired percentage of water. Therefore, the total volume of the new mixture will be 125 + x gallons.

3. Set up an equation based on the desired percentage of water:
- After adding x gallons of water, the new mixture will contain 25% water, so we can write:
25% of (125 + x) = 25/100 * (125 + x) = 31.25 + 0.25x gallons of water
- We want this to be equal to the amount of water in the new mixture, which will be the sum of the original 25 gallons of water plus the x gallons of water added:
25 + x gallons of water

4. Set up the equation and solve for x:
31.25 + 0.25x = 25 + x
0.75x = 6.25
x = 8.33 gallons of water (rounded to two decimal places)

Therefore, we need to add 8.33 gallons of water to the mixture to achieve the desired percentage of water. The correct answer is option D, 8.33 gals.

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