Question

PERCENTAGES QUESTION :)
Two beakers of equal volume
Beaker A contains 30% salt
Beaker B contains 10% salt

How many ounces of solution A should be added to solution B, so that the resulting solution is 20% salt?

Answer 1

so far, I let x be the amount of solution in Beaker A.
then, 30% of that is the amount of salt in A....same for B...

Answer 2

Let's try 10 liters.
10 liters of A has 3 litres salt.
10 liters of B has 1 litres salt.
You end up with 20 liters with 4 litres salt.
4 litres out of 20 litres is 20%

Answer 3

Okay, yep, I;m following so far....

Answer 4

Since the concentration you want is exactly the average of the two concentrations you start with, the same amounts of A and B are used.

Answer 5

Oki doki, that makes sense - there might be a problem with the worked solution – its talking about ounces, and I have no information about how many ounced the beakers started out with....

Answer 6

Use ounces where I used litres.

Answer 7

heres the part that dosnt make any sense to me in the worked solution: "the resulting solution will be 50 + x ounces and its concentration of salt will be 20%(50+x)....

Answer 8

im guessing instead of your 10L base, theyve used 50 ounces?

Answer 9

Is there any info missing from the question you posted?
Where does the number 50 come from in the solution?

Answer 10

thats exactly my problem...

Answer 11

Beaker A has x ounces of 30% salt solution.
Beaker B has x ounces of 10% salt solution.
(Both beakers have x amount because we are the beakers have equal volume.)

Answer 12

Yes. Corecct

Answer 13

x ounces of solution B has 0.1x ounces of salt.

Answer 14

Yep

Answer 15

Now we need to start adding solution A to solution B until we have a new solution that is 20% salt.

Answer 16

Let's say we add y ounces of solution A to solution B.

Answer 17

To do that, we need to find the volume in A containing a concentration of 10%?

Answer 18

Okay, yep

Answer 19

y ounces of solution A has 0.3y ounces of salt

Answer 20

correct

Answer 21

We will have a total of salt:
0.3y + 0.1x
Ok?

Answer 22

Yep, all good so far. Thanks for going through it with me.

Answer 23

Next, we will have a total amount of solution of:
x + y
Ok?

Answer 24

Yes.

Answer 25

We want the new solution to have a concentration of 20% salt.
20% = 0.2

That means

\(\dfrac{0.3y + 0.1x}{x + y } = 0.2\)

Answer 26

Okay, cool.

Answer 27

Now let's solve that equation and what we get.

Answer 28

x=y?

Answer 29

\(\dfrac{0.3y + 0.1x}{x + y } = 0.2\)

\(0.3y + 0.1x = 0.2(x + y)\)

\(0.3y + 0.1x = 0.2x + 0.2y\)

\(0.1y = 0.1x\)

\(y = x\)

Correct.

Answer 30

Since we chose x to be the amount of solution B and y to be the amount of solution A, we see the amounts must be the same no matter how much each beaker has.

Answer 31

Understood

Answer 32

Great.

Answer 33

So do you think that they made x=y=50 ounces?

Answer 34

in the solutions?

Answer 35

That's what I am thinking.

Answer 36

Yeah, okay. Well thanks for going through it with me in detail. Appreciate your work :)

Answer 37

Before the part of the solution you quoted above mentioning 50 + x, was there any mention of 50?

Answer 38

You're welcome.

Answer 39

their equation is exactly what you had, except they made 50=y for some reason:
10%50 + 30%x = 20%(50+x)

I understand the equation now, thank you.

And no. No mention anywhere of 50 :(

Answer 40

Also, just wondering if you know how to change the username on open study? i can find the change passwords under settings, but is it even possible to change usernames?

Answer 41

I guess they just assumed they would use 50 ounces of one solution, and then they found how many ounces of the other solution they needed. It turns out to be 50, of course, bec now we know it's the same amount of both solutions.

Answer 42

I don't know if you can change username in OS.

Answer 43

Yes, I reckon you're right on that one.

Okay then, thank you!