Question

How many liters of water must be added to 12 L of a 40% solution of alcohol to obtain a 30% solution? can you help me write the equation?

Answer 1

x + 12 = y
0x + .40(12) = .30y

Answer 2

If you want an explanation, let me know

Answer 3

i dont understand please explain

Answer 4

The first equation represents the amount of liquid in Liters in each beaker. In the first beaker, you have x liters of liquid (water). In the second beaker you have 12 liters of liquid (a mixture of alcohol and water). The third beaker, y represents a combination of both liquids together.

Answer 5

The second equation, represents the percentage of alcohol solution in each beaker. In the first beaker, there is 0% alcohol in the beaker, hence, 0x which means that there no alcohol, just water. The second beaker has 40% alcohol, hence .40(12) which means the same as 40% of 12 liters. The third beaker has .30y or 30 percent of however many liters of a mixture there is.

Answer 6

0x+4.8=30y
-4.8=30y-4.8
0x=30y-4.8
now how do i solve for x?

Answer 7

Let me post the solution for you

Answer 8

okay thank you but could you work it out also please?

Answer 9

That's exactly what I meant by "solution". What did you think I meant?

Answer 10

I thought you were only going to provide the answer, so I wanted to be sure all the information was there so I can learn from it. Thanks again.

Answer 11

x + 12 = y
0x + 4.8 = .30y

x + 12 = y
4.8 = .30y

y = 12 + x
y = 4.8/.30

y = y

12 + x = 4.8/.30

.30(12 + x) = 4.8

3.6 + .30x = 4.8

.30x = 4.8 - 3.6
.30x = 1.2

x = 1.2/.30
x = 4

y = 4 + 12
y = 16

Answer 12

solution \(\ne\) answer

Answer 13

Solution = detailed description of the steps from the problem to the answer.
Answer = numerical representation of variables of the problem set

Answer 14

thank you

Answer 15

thank you for your help Hero but can someone else maybe help i just dont follow all of your steps

Answer 16

I can explain it to you in vyew

Answer 17

what?

Answer 18

The way I thought about it is:



We need to add water to make the percentage of the alcohol go down, but the quantity of alcohol will remain the same, just more water is added. Therefore the total amount of Liters will rise.

So 30% of the total solution of: 12 Liters of Solution + 'X' amount of water added will still be equal to 4.8 liters of Alcohol, because the quantity of alcohol does not change. Only the percentage of alcohol of the total solution does.

Algebraically: .30 * (12 + x) = 4.8

If you solve that, you will get x = 4, which means you need to add 4 Liters of Water to the entire thing to make the 4.8 liters of Alcohol 30% of the entire thing.