How do I resolve this?

A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the rati

AnnyKZ [126]

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 <em>20%</em> 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%.

3 0

2 years ago

Read 2 more answers

The correlation coefficient for the ages of drivers in a driver safety class and the number of traffic violations they have rece

Doss [256]

A correlation coefficient is always a value in between -1 and 1
The closest a coefficient to -1, the correlation is a strong negative correlation
The closest a coefficient to 1, the correlation is a strong positive correlation
The closest a coefficient to 0, there is no correlation at all

The coefficient -0.61 shows a strong negative correlation
This means that the relationship between the age and the violation is an inverse relationship; as age increases, violation decreases

Answer: option C

7 0

3 years ago

Four students are called to sit in four chairs on

bekas [8.4K]

There is a 50/50 chance Bob and Wanda will sit next to each other.

8 0

3 years ago

Suppose that the function f is defined, for all real numbers, as follows.

Veseljchak [2.6K]

The solutions of the function are:

When f(x) = -4, the solution is -4
When f(x) = -2, the solution is -5/2
When f(x) = 0, the solution is -1

<h3>How to solve for the equation </h3>

The equation is given as

$\frac{3}{4} x-1\\\\$

When x = -4

3/4 * -4 -1

= -12/4 - 1

= -4

When x = -2

3/4*(-4) - 1

= -6/4 - 1/1

Take the lcm

-10/4

= -5/2

When x = 0

3/4(0) - 1

= -1

When f(x) = -4, the solution is -4

When f(x) = -2, the solution is -5/2

When f(x) = 0, the solution is -1