Question

A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the ratio of alcohol to water is 2:3. Each glass is emptied into a third glass. What is the ratio of alcohol to water in the final mixture?
A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the ratio of alcohol to water is 2:3. Each glass is emptied into a third glass. What is the ratio of alcohol to water in the final mixture?

Answer 1

Answer:

3:7

Step-by-step explanation:

So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or 20% is alcohol. So let's just say that x=alcohol and y=water, this means that: $x+y=c$  where c is the total amount in the glass. This means that: $x=0.20c$

Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: $j+k=c$ and that: $j=0.40c$.

So if we're going to add the two glasses, we simply add the two sides, and get: $j+x+k+y=2c$. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: $(0.4c+0.2c)+x+k=2c$ Now we can add like terms to get the equation: $0.6c+y+k=2c$. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.

Answer 2

Answer:

3 : 7

Step-by-step explanation:

We can do this question using a easier way.

For example, A glass contains sugar and water, the ratio to sugar to water is 2 : 5. And the second glass's sugar to water is 2 : 3. The mixture of the first glass is 200 mL. The mixture of the second glass is the same as the first glass.

This kind of glass question, is very important to Math.

Try using this to solve this question.