I really suck at math, can you pls help me solve this..?

Question

How many quarts of a 20% salt solution must a chemist mix with a 40% salt solution to make 40 quarts of a 25% slat solution?

I'm going to have a test on questions like this soon and idon't understand any of it. Can u help me understand and solve this question.

Answer 1

Alright, to start off, we have an unknown quantity of 20% salt solution. Let this equal our variable, x. The number of quarts of 40% salt solution will be our variable, y.

Instead of using percents, I'll use decimals.

So, what we have here is:

0.20x + 0.4y = (0.25)(40)

The "(0.25)(40)" term is the amount of salt we have in solution.

Keep in mind that x + y = 40. The amount of solution x plus the amount of solution y must equal 40 quarts.

x + y = 40
0.20x + 0.4y = 10


Use elimination.

x + y = 40
(-5)[0.20x + 0.4y] = -5(10)

x + y = 40
-x - 2y = -50


Add the two lines together to eliminate the variable x.

x + y = 40
-x - 2y = -50
___________
..... -y = -10

y = 10

and since x + y = 40

x + (10) = 40

x = 30


And to check:

0.20x + 0.4y = 10
0.20(30) + 0.4(10) = 10
6 + 4 = 10
it all works out!

You need 30 quarts of 20% salt solution and 10 quarts of 40% salt solution.

Answer 2

Use x for the number of quarts of weaker solution and y for the stronger. You need a total of 40 quarts so this gives you
x + y = 40 or y = 40 - x. The final strength needs to be 25% so this means 20x + 40y = 25*40. You now replace y by 40 - x in this equation and solve it. Try to finish it before looking at any other answer left here.

Answer 3

1) If you add 1 quart of 20% SS and 1 quart 40% SS , you will get 2 quarts 30% SS. That is 20% + 40% = 60%/2 = 30%
This means that you cannot mix 20% SS with equal amount of 40% SS to get 25%
2) If you add 2 quarts of 20% SS with 1 quart of 40% SS, you will get 3 quarts 26.667 % SS. That is 20% + 20% + 40% = 80%/3 = 26.667% SS
3) If you add 3 quarts of 20% SS with 1 quart of 40% SS, you will get 4 quarts of 25% SS. To make 40 quarts of 25% SS, you have to multiply the amount of 20% SS and 40% by ten.
That is 3 x 10 = 30 quarts of 20% SS and 1 x 10 = 10 quarts of 40% SS.
Therefore, 30 quarts of 20% salt solution and 10 quarts 40% salt solution will make 40 quarts 25% salt solution.

For mathematical expression, I will figure it out later.

Answer 4

Amount of 20% solution=x quarts
Amount of 40% solution=y quarts
Total number of quarts=40
So x+y=40----->1
Also (20x+40y)/x+y=25
That is x+2y=50------->2

Solve the equations to get x and y as 30 and 10 respectively.

Answer 5

Let x quarts of 20%salt solution be mixed with 40-x quarts of 40% salt solution to make 40 quarts of 25% salt solution
Qty.of saltin x quarts 20%soln=0.2x [20%=0.2]
qty of salt in 40-x quarts of salt solution
=0.4(40-x) [40%=0.4]
=16-0.4x
qty of salt in40 quarts of 25%salt solution
=0.25*40 [25%=0.25]
=10
according to the problem,
0.2x+16-0.4x=10
=> -0.2x=10-16= -6
=>x= -6/-0.2=30
therefore,30 quarts of 20% solution should be mixed with40-30or 10 quarts of 40% solution.

Answer 6

Let x quarts of 20% salt solution be needed
0.2x+0.4(40-x)=40(.25)
0.2x+16-0.2x=10
-0.2x+16=10
-0.2x=10-16
-0.2x=-6
-1(-0.2x)=-1(-6)
0.2x=6
x=30
30 quarts of 20% salt solution is needed.

Answer 7

Try reading through the answers you've received to previous questions. It really isn't all that hard to understand if you try to understand it instead of just copying someone else's work.