One canned juice drink is 25% orange juice another is 5% orange juice. How many liters of each should be mixed together in order to get 20L that is 24% orange juice?
How many liters of the 25% orange juice should be in mixture?
How many liters of the 5% orange juice should be in mixture?
How can I solve this problem, or what is the best method??
I started the problem and got stuck, I first started with x= amount of 25%
and y= amount of 5%
x+y=20L
0.25x+0.05y=54
100(0.25x+0.05y)=100(54)
25x+5y=5400
is this correct so far? and I am stuck here...
Patience .
http://www.jiskha.com/display.cgi?id=1257456892
You have made a good start in setting up the equations. Let's go step by step to solve the problem.
Let's define:
x - liters of the 25% orange juice
y - liters of the 5% orange juice
We have two equations based on the information given:
Equation 1: x + y = 20L (The total volume of the mixture is 20L)
Equation 2: (0.25 * x) + (0.05 * y) = 0.24 * 20L (The total orange juice content in the mixture is 24% of 20L)
Now, let's simplify Equation 2:
0.25x + 0.05y = 4.8
To get rid of the decimals, we can multiply both sides of Equation 2 by 100:
100 * (0.25x + 0.05y) = 100 * 4.8
25x + 5y = 480
Now, you have the system of equations:
Equation 1: x + y = 20
Equation 3: 25x + 5y = 480
To solve this system, you can use the method of substitution or elimination. Let's use the method of substitution:
From Equation 1, you can isolate x by subtracting y from both sides:
x = 20 - y
Now substitute this value of x in Equation 3:
25(20 - y) + 5y = 480
500 - 25y + 5y = 480
-20y = -20
y = 1
Now substitute the value of y back into Equation 1 to find x:
x + 1 = 20
x = 19
So, the solution is x = 19 liters of the 25% orange juice and y = 1 liter of the 5% orange juice.
Therefore, you should mix 19 liters of the 25% orange juice and 1 liter of the 5% orange juice to get a 20-liter mixture that is 24% orange juice.