A glass contains vinegar and water in the ratio 1:3. Another glass twice the capacity of the first has vinegar and water in the ratio 1:4. If the contents of both glasses were mixed together in another container what is then the ratio of vinegar to water?
For vinegar and water respectively:
Let first glass have volume 5 = 5/4 + 15/4
Let second glass have volume 10 = 10/5 + 40/5
( 5/4 + 10/5) : (15/4 + 40/5) = 65 : 235 = 13 : 47
- Call the capacity of the first glass $x$. What is the capacity of the second one, that's twice as big?
For the first glass, the ratio of vinegar to water is $1:3$. This means the amount of vinegar is $x/4$ and the amount of water is $3x/4$.
- What would be the amount of vinegar in the second container? (Remember, it's twice as big.)
- What is the amount of water in the second container?
- What is the total amount of vinegar after the containers are mixed?
- What is the total amount of water after the containers are mixed?
- What, then, is the ratio after the mixing?