Containing solution of juice.

Question

Solution contaning 30% juice is mixed with a solution containing 10% juice to make 100 gallons of soluion that is 12% juice. How much of 30% solution was use?

Answer 1

Hello again, T -- since 12% is so close to the 10% juice, we know relatively little of the 30% stuff is used ... naturally test the 90g-10g mix as a starting point :)

Answer 2

Titaree:

Let x = number of gallons in the 1st solution.

Let y=number of gallons in the 2nd solution.

From the info provided, we can write an equation: .30x+.10y=.12(100)  or .3x+.1y=12  (A)

We also know that the sum of the two solutions is 100 (gallons) or  x+y=100  (B)

We can then solve the two simultaneous equations A & B:

We can first solve equation B for y, to get:  y=100-xWe can then substitute this for y in equation A, to get:  .3x+.1(100-x)=12 or .3x+.1(100)-.1x=12

Solving this for x, we get:  .2x=12-10  or .2x=2  or x=10 = number of gallons in first (30%) solution (final answer).

You can carry this further to solve for y (the number of gallons in the second solution).  The answer comes out to be 90.

You can then check your work by plugging the values for x and y back into equations A & B.

Answer 3

There is a quick way in doing such a problem. The concept is inverse proportion to the difference between the initial concentration and the final concentration.

The difference between 30 and 12 is 18.

The difference between 10 and 12 is 2.

The amount of 30% juice required is 100*2/(18+2) = 10 gallons.

 

Answer 4

The final mixture is 100 gallons containing 12% juice.

This means that 12 gallons of juice is there in the final mixture

Let x be the number of gallons of mixture 1 (30% mixture).  Since the total final mixture is 100 gallons, it contains (100-x) gallons of 10% mixture.  

x gallons of the 30% mixture will contain 0.3x gallons of pure juice

(100-x) gallons of 10% mixture will contain (100-x)*10/100 or (10-0.1x) gallons of pure juice

Total amount of pure juice is therefore 0.3x+10-.1x or 10+0.2x gallons

But from the first step in the proof, we know that the total amount of juice is 12 gallons

Therefore 10+.2x=12 or x=10

So we mix 10 gallons of 30% mixture with 90 gallons of 10% mixture to get a mixture of 12% juice