Question

Juice has 30% oj and another has 10% oj. How many liters of each is needed to get 20L at 16% oj?

Answer 1

posted above my plea

Answer 2

x= amount of 30%
20-x= amount of 10%
.3x+.1(20-x)=.16(20)

Answer 3

Do you understand the equation and can you solve it?

Answer 4

kind of understand - getting confused a little

Answer 5

greatly due to frustration I am sure

Answer 6

If you have 20 ounces of candy and 50% of it is M&M's then .5(20) = amount of M&M's
so if you have x L of solution and it is 30% OJ, then .3(x)= amount of OJ

Answer 7

Starting amount of OJ + added amount OJ= final amount of OJ

Answer 8

\[.3x+.1(20-x)=.16(20)\]
\[.3x+2-.1x=3.2\]
\[.2x=1.2\]
x=6 L of 30 % OJ
20-6=14 L of 10% OJ

Answer 9

plz dont laugh - on the second line where did the 2 come from - lookin at my work I think that is where I was messing up

Answer 10

Juice has 30% OJ and another has 10% OJ. How many liters of each is needed to get 20L at 16% OJ?

To answer these “mixture problems”, we need to set up some equations. Once we have the equations, we solve them.

Part I What are the equations?

Start with the question
“How many liters of each is needed to get 20L?”

Think, “I add some of juice A and some of juice B to get 20 L” which is written as
A+B= 20
We don’t know the amounts (yet), but it should make sense. A liters from the 30% juice plus B liters from the 10% juice must equal 20 liters.

Next, the key idea or insight. If you have 30% OJ this means 30% of the juice is pure OJ and 70% (100% - 30%) is pure water.
Use this idea to figure, if I have 20 liters of 16% OJ, then 16% of 20 liters is pure OJ. As an equation:
0.16*20 liters= 3.2 liters pure OJ

Apply this same idea to A liters of the 30% OJ: if I have A liters of 30% juice, then I have 0.30*A of pure OJ. And for B liters of the 10% OJ, I have 0.1B liters of pure OJ.

So, thinking just about the (pure) OJ:
0.3A + 0.1B = 3.2
This says that the amount of OJ in A liters of 30% juice plus the amount of OJ in B liters of 10% juice must add up to 3.2 liters in the final mix.

Part II Solve the equations

0.3A+0.1B= 3.2
A+B= 20

multiply the first equation by 10, to get rid of the decimals.
We get
3A+B= 32
A +B= 20

Subtract the two equations, term by term
(3A-A)+(B-B)=(32-20)
2A= 12
A= 6
Now use one of the two equations to find B. Use the simpler one,
A+B=20
6+B=20
B=14

The final answer is, 6 liters of the 30% juice, and 14 liters of the 10% juice.