Question

One canned juice drink is 15% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 10L that is 11% orange juice?

Answer 1

Hey, I lost track of you.

Answer 2

It uses elimination again
Let A be 15% juice and B is 5% juice

A+B = 10
0.15A + 0.05B = 0.11*10 = 1.1
Multiply 2nd equation by 100 to get rid of decimals

A+B = 10
15A + 5B = 110

Answer 3

Okay, that went right over my head...LOL

Answer 4

dumbunny, you're like me with Calculus

Answer 5

haha I wouldn't touch Calculus with a 100 foot pole!

Answer 6

Of course I aced Calculus I and II, classroom courses...still had issues though

Answer 7

I would never have been able to pull off what some people do here.

Answer 8

I am in awe of about 99 percent of the people here.

Answer 9

So how many liters of the 15% orange juice should be in the mixture and how many liters of the 5% orange juice should be in the mixture?

Answer 10

ok sorry i was away
A is amount of drink that is 15% orange juice
B is amount of drink that is 5% orange juice
So 0.15A and 0.05B represent the actual amount of orange juice in either drink.
By mixing them together you get a total amount 10L
You want this mixture to have 11% orange juice...so 0.11*10 = 1.1
Now set up balanced equations
First equation is concerned with quantity of drink
A + B = 10
2nd equation is concerned with actual amount of orange juice
0.15A + 0.05B = 1.1

Think of it this way, if there is more 15% drink then mixture will be closer to 15% than 5%, If there is more 5% used then mixture will be closer to 5% than 15%

does that make more sense?

Answer 11

No it doesn't. Sorry, I know I am pretty pathetic when it comes to this stuff.

Answer 12

ok lets do an example:
Lets say we mix 100L of each drink.
15% of 100 = 0.15*100 = 15
5% of 100 = 0.05*100 = 5
This means we are mixing 15L of orange juice with 5L of orange juice
total amount of mixture:
100 + 100 = 200
total amount of orange juice
15 + 5 = 20
Now to find out the percentage of orange juice in mixture, divide
20/200 = 1/10 = 0.1 = 10%

Ok so if the question was how many liters to be mixed to get 200L of 10% orange juice.
the answer would be 100 of A and 100 of B.

Answer 13

So you would mix equal amounts? No, that can't be right. My mind is just a blank right now. I have been working on this quiz for the past 8 hours.

Answer 14

yes if you wanted mixture to be 10% which is exactly in between 5% and 15%.
This problem is looking for 11%
is 11 closer to 15 or 5?

Answer 15

15

Answer 16

right, so you know that there will be more of the 15% in the mixture
They have to add up to 10, half of 10 is 5
so one must be greater than 5 while the other less than 5

Answer 17

6 and 4

Answer 18

yes

Answer 19

So 6 liters of the 5% and 4 liters of the 15%

Answer 20

for this one it works out nicely, 6 and 4
most times you need to go through and solve the equations to get exact answer

check your answer
does
0.15*6 + 0.05*4 = 1.1 ??

Answer 21

yes it does

Answer 22

then thats your solution :)
wait which one should have more, 15% or 5% ?

Answer 23

the 5%

Answer 24

is it closer to 11% ?

Answer 25

no

Answer 26

whichever one is closer to the mixture percentage will always have more

Answer 27

So it would be 6 liters of the 15% and 4 liters of the 5% ??

Answer 28

yes

Answer 29

okay, got it. THANK GOD! Thank you very much.

Answer 30

your welcome