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 9% orange juice?
x liters of .15 oj
then (10-x) of .05 oj
amount of oj in final = .15 x + .05(10-x)
= .09 *10 = .9
so
.15 x +.5 - .05x = .9
.1 x = .4
x = 4 liters of .15
then
6 liters of .05
To find the solution to this problem, we can set up a system of equations. Let's assume x represents the amount of the 15% orange juice and y represents the amount of the 5% orange juice.
The total volume of the mixture is 10L, so we can write the first equation as:
x + y = 10 (equation 1)
Next, we can determine the amount of orange juice in each mixture:
For the 15% orange juice, since 15% of x liters are orange juice, the amount of orange juice is 0.15x.
For the 5% orange juice, since 5% of y liters are orange juice, the amount of orange juice is 0.05y.
The total amount of orange juice in the mixture should be 9% of the 10L, so the second equation is:
(0.15x + 0.05y) / 10 = 9/100 (equation 2)
To solve this system of equations, we can use substitution or elimination method. Here, we'll use the substitution method.
From equation 1, we can express x in terms of y:
x = 10 - y
Substituting this value of x into equation 2, we have:
(0.15(10 - y) + 0.05y) / 10 = 9/100
Simplifying the equation:
(1.5 - 0.15y + 0.05y) / 10 = 9/100
(1.5 - 0.1y) / 10 = 9/100
Cross-multiplying:
100(1.5 - 0.1y) = 10(9)
150 - 10y = 90
15 - y = 9
Solving for y:
y = 15 - 9
y = 6
Now substituting this value of y back into equation 1, we can find x:
x + 6 = 10
x = 10 - 6
x = 4
Therefore, to get 10L of a mixture that is 9% orange juice, you should mix 4L of the 15% orange juice with 6L of the 5% orange juice.