You have 2.8 gals of 80% solution and you need some 60% solution. How much 30% solution do you need to mix wit

Question

You have 2.8 gals of 80% solution and you need some 60% solution. How much 30% solution do you need to mix with the 2.8 gals of 80% to achieve this result?

Answer 1

Hi,

80%(gallons of A) + 30%(gallons of B)=60%(gallons of A + B)

.80(2.8) + .30x = .60(2.8 + x)

2.24 + .3x = 1.68 + .6x

.56 = .3x
28/15 or 1.86666666 = x

1.86666666 gallons of 30% solution need to be added.


Another interesting way to look at a mixture problem is to do this:

You want to mix 80% solution with 30% solution to make a 60% solution. Put these numbers on a number line.
.30...40....50....60....70....80
-+-----+-----+-----+-----+-----+
These are 30 apart out of a total difference of 50.
.|<=========>.|

30/50 is 3/5 of the distance. From 60 up to 80 is 20/50 or 2/5 of the distance. Now trade the 3/5 and 2/5 so the 2/5 is now on the 30% side and 3/5 is on the 80% side. What this means is that you will need 2/5 of the final mixture to be 30% solution and 3/5 of the final mixture to be 80% solution, which is 2.8 gallons. Make a proportion to solve.

2.8........x
----..=..------
3/5.......2/5


2.8........x
----..=..------
.6......._.4

.6x = .4(2.8)
.6x = 1.12
x = 1.86666666


I hope those help!! :^)

Answer 2

you have 2 equations, one for the total amount, the A's, and one for the percentages of the A's which are the active ingredients. the 2 are embedded, so the basic equation for almost all problems like this looks like
p1A1 + p2A2 = p3(A1 + A2)

80%(2.8) + 30%(x) = 60%(2.8+x)
80%(2.8) + 30%(x) = 60%(2.8) + 60%(x)
80%(2.8) - 60%(2.8) = 60%(x) - 30%(x)
20%(2.8) = 30%x
2.8 = 1.5x
x = 1.87 gal.

notice how I used distributive property to avoid any serious arithmetic until the last step.

Answer 3

Let x be the amount of 30% solution needed.
Do the balance of the solute:
the initial amount of solute = the final amount of solute
2.8(.8)+x(.3) = (2.8+x)(.6)
Solve for x,
x = 2.8(.2)/.3 = 1.87 gals

Answer 4

Let g = no. of gallons of 30% solution.

Equation (Answer):
80%(2.8) + 0.3(g) = 60%(2.8 + g)
2.24 + 0.3g = 1.68 + 0.6g
2.24 - 1.68 = 0.6g - 0.3g
0.56 = 0.3g
0.56 / 0.3 = g
g = 28/15 or 1 13/15 or 1.86667

Answer 5

Let x gallons of 30% soln to be mixed with 2.8 gallons of 80% soln to make 2.8+x gallons of 60% soln
By the problem,
0.80*2.8+0.30x=0.60(2.8+x)
or,2.24+0.30x=1.68+0.60x
or,0.30x-0.60x=1.68-2.24
or, -0.30x= -0.56
or,x=-0.56/-0.30=1.867 gallon
hence 1.867 gallon of 30% soln is to be mixed