SOLUTION: Please help: 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 7% orange juic

Algebra ->  Functions -> SOLUTION: Please help: 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 7% orange juic      Log On


   

Question 1043905: Please help:
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 7% orange juice?
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let
x = amount of the juice drink that is 15% orange juice
y = amount of the juice drink that is 5% orange juice
both amounts are in liters (L)


---------------------------------------------------------


We have x liters from one can and y liters from another can. We mix them together and together they make 10 liters of juice. So x+y = 10 is our first equation.


We have x liters of the 15% orange juice. The amount of pure orange juice is 0.15x liters.


We have y liters of the 5% orange juice. The amount of pure orange juice is 0.05y liters.


In total, those amounts combine to 0.15x+0.05y. We want 10 liters of 7% orange juice. So we want 10*0.07 = 0.7 liters of pure orange juice.


Therefore, the two amounts must be the same (ie equal). So 0.15x+0.05y = 0.7 is the second equation


---------------------------------------------------------


To summarize so far, we have these two equations


x+y = 10
0.15x+0.05y = 0.7


Let's focus on the first equation for now. Solve for y to get...


x+y = 10


x+y-x = 10-x ... subtract x from both sides


y = 10-x


Now that y is isolated, we can plug this into the other equation


0.15x+0.05y = 0.7


0.15x+0.05( y ) = 0.7


0.15x+0.05( 10-x ) = 0.7 ... replace y with 10-x. Now solve for x.


0.15x+0.05(10)+0.05(-x) = 0.7


0.15x+0.5-0.05x = 0.7


0.10x+0.5 = 0.7


0.10x+0.5-0.5 = 0.7-0.5


0.10x = 0.2


0.10x/0.10 = 0.2/0.10


x = 2


We finally know the value of x. Use this to find y.


y = 10-x


y = 10-2 ... replace x with 2


y = 8


----------------------------------------------------------
----------------------------------------------------------


In the end, we found that x = 2 and y = 8. Recall that at the very top we stated that

x = amount of the juice drink that is 15% orange juice
y = amount of the juice drink that is 5% orange juice


so this means that we must mix 2 liters of the 15% juice drink with 8 liters of the 5% juice drink.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Please help:
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 7% orange juice?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

From the condition, you have this system of two equations in two unknowns

    x +     y = 10        (1)   (the total volume balance)
0.15x + 0.05y = 0.07*10   (2)   (the amount of the pure juice in 10 L of mixture)

or equivalently

  x +  y = 10             (1')   
15x + 5y = 70             (2')   
     
Solve it by any method, substitution or elimination.

Answer.  x = 2 L of the 15% juice;  y = 8 L of the 5% juice.

On mixture word problems see the lessons
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Typical word problems on mixtures from the archive
in this site.