how many ml of vinegar must be added to 20ml of a 10%-vinegar solution to make it a 25%-vinegar solution?

Answer 1

20(10) +x(100) = (20+x)25

200+ 100x = 500 +25x

75x = 500-200 = 300

x = 300/75 = 4 mL of 100% vinegar mixed with 20 mL of 10% to get 24 mL of 25%

100 is within 75 of 25

10 is within 15 of 25

75/15 = 5

20/4 = 5

You need 5 times as much 10% as 100% because it's 5 times as close to 25%

Answer 2

Let us first calculate volume of vinegar and water present in 20 ml of 10% vinegar solution.

Volume of vinegar in solution = 10% of 20 ml

= 0.1*20

= 2 ml

Volume of water in solution = 90% of 20 ml

= 0.9*20 = 18 ml

Let x ml be the volume of vinegar added in solution

So now, volume of vinegar in new solution = 2 + x

And volume of new solution = 20+ x

The new solution has 25% vinegar

That means, (2+x) is 25% of (20+x)

2 + x = 0.25(20+x)

2 + x = 5 + 0.25x

x - 0.25x = 5-2

0.75x = 3

x = 3/0.75

 = 4 ml

Hence, 4 ml of pure vinegar needs to be added to the solution