Question

how many liters of a 60% acid solution must be mixed with a 30% acid solution to get 300L of a 50% acid solution?

Answer 1

These mixture problems are easy when you create a table. Let's do that.
Let x = 30% acid solution and y = 60% acid solution

Answer 2

So from this table you add up the total liters which is x + y = 300
And the total solution is 0.30x + 0.60y = 150

In the table I should had put the total liters as 300 L instead of x + y because x + y that sum equations a total of 300 liters.

So using those two equations you can find x and y. You can use substitution of elimination method to find the solution.

Answer 3

how do i solve the equation

Answer 4

would it be 0.30x+0.60y=150 or 300?

Answer 5

Let's do substitution method.
x + y = 300. Let's use this equation. Solve for y. It doesn't have to be y it could b x but I just choose y for this purpose.

y = 300 - x

Then you take that equation plug it into this one 0.30x + 0.60y = 150

So you get 0.30x + 0.60 (300 - x) = 150.

Solve for x and once you have x then you plug into either equation
0.30x + 0.60y = 150
or
x + y = 300 to find y.

Answer 6

i dont know how to find y

Answer 7

Plug x into this equation y = 300 - x

Answer 8

so it would be y=300-0.30?

Answer 9

No you have to solve this equation 0.30x + 0.60 (300 - x) = 150 to find x.
What step did I do you find most confusing?

Answer 10

how do i get the answer ? im still confused

Answer 11

1.) x + y = 300
2.) 0.30x + 0.60y = 150

So you solve for one of the variables. Because you cannot solve an equation with two unknowns. So equation 1.) I will solve for y. When I do equation 1.) becomes y = 300 - x
Then I take that equation plug it into this equation 0.30x + 0.60y = 150. When I do that I get the following

0.30x + 0.60 (300 - x) = 150

Solve for x.

You use your algebra. So you distribute the 0.60 (300 - x ) = 0.60*300 - 0.60x

0.30x + 180 - 0.60x = 150

Combine like terms

-0.30x + 180 = 150
subtract 180 on both sides

-0.30x = -30

divide -0.30 on both sides to solve for x

x = 100

Now you know x = 100 plug x into the equation x + y = 300
to find y

Answer 12

is it 100+y=300?

Answer 13

Yes. Now solve for y and you will have your solution.

Answer 14

can you write it like this y+100=300?

Answer 15

Yeah you can if you want. The idea is to get y by itself
100+y=300
You subtract 100 on both sides

100 - 100 + y = 300 - 100

y = 200

Answer 16

is that the answer to the question??

Answer 17

yes.
x = 100 and y = 200

Answer 18

so 200 liters of a 60% acid solution must be used?

Answer 19

That is correct