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

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)   (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)

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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

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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

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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(52786)   (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.

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