Help with Algebra!?

Question

How many liters of a 40% solution must be mixed with 60 liters of an 80% solution to get a 70% solution?

Please explain !

Answer 1

Let x = liters of 40% solution.

40%*x + 80%*60 = 70%*(x + 60)

solve for x

Answer 2

V total liters with 40%
W total of liters with 80 % ( thus 60 liter )
X total of liters of 70% ( X = W + V )

solve this : the particular 'thing' in the solution divided by the total vilume is 70%
(V*0.4 + W*0.8) / (V+W) = 0.7

everything is known except for V
solve V and then set X = V + W ( with W = 60 is given ).

.

Answer 3

x= 40% solution

40% x + 80%(60)=70%(X+60)

40%x+48=70%x+42
40%x-40%x+48=70%x-40%x+42
48=30%+42
48-42=30%+42-42
6=30%x

30%x=6
30/100=6/x
30x=600
x=20 liters of a 40% solution

Answer 4

Let x be the number of liters.
When you mix the two solutions, you have x + 60 liters.
Then:
40x + 60*80 = (x + 60)70
Multiply out:
40x + 4800 = 70x + 4200
Subtract 4200 from each side:
40x + 600 = 70x
Subtract 40x from each side:
600 = 30x
Divide by 30:
x = 20.
You need 20 liters of 40% solution.

Answer 5

Well, you substitute "how many liters?" with "a." Then you just change the words into a mathematical equation:

"LITERS of a 40% solution" = a*0.40 = 0.4a
"60 LITERS of an 80% solution" = 60*0.80 = 0.8*60
"70% solution made with HOWEVER MANY LITERS of the first solution PLUS 60 LITERS of the second solution." = 0.7*(a+60)

0.4a + 0.8(60) = 0.7(a+60)
0.4a + 48 = 0.7a + 42
6 = 0.3a
20 = a

you need 20 liters of 40% solution

to verify:
20*0.4 + 60*0.8 = 0.7(20+60)
8 + 48 = 0.7(80)
56 = 56

Answer 6

let N = number of liters of 40% solution

Use Number1 * Pct1 + Number2 *Pct2 = (Number1 + Number2) * Pct mixed

N x 0.4 + 60 x 0.8 = (N+60) x 0.7

0.4 N + 48 = 0.7N + 42

6 = 0.3N

N = 20

You need 20 liters of 40% solution.

Answer 7

Suppose you have m liters of 40% solution. Then

[0.4m + 0.8(60)]/(m+60) = 0.7

0.4m + 48 = 0.7m + 42

0.3m = 6

m =20

Answer 8

0.4(x) + 0.8(60) = 0.7(x + 60)
2x/5 + 48 = 7x/10 + 42
-42 -42
2x/5 + 46 = 7x/10
*10 *10
2x + 460 = 7x
-2x -2x
5x = 460
/5 /5
x = 92
92 liters

Answer 9

20L
I think!
(a+48)/(b+60)=0.7
where a is the amount in the solution, b is the total volume,
a/b=0.4 it's 40% solution

a+48=0.7b+42
a+6=0.7b
a+6=0.7(a/0.4)
a+6=1.75(a)
a(1.75-1)=6
0.75(a)=6
a=8

a/b=0.4

8/b=0.4
=> b=20

so a/b=8/20
so 20L is required?!

Answer 10

its a stupid question that you will NEVER use after high school.