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...
Where does the 54 come from ?
The second equation should have been
.25x + .05y = .24(20)
times 100 --->
25x + 5y = 480
now multiply your first by 5
5x + 5y = 100
subtract this from the other one...
20x = 380
x = 19
then y = 1
ohhh... thank you.... no wonder why I got stuck.. I missed a step and miscalculated thank you so much
Yes, you're on the right track so far. You have correctly set up the system of equations:
x + y = 20
0.25x + 0.05y = 0.24 * 20 (since we want 24% orange juice in the final mixture)
Now, let's continue solving the system of equations. We'll use the method of substitution.
From the first equation, we can isolate x:
x = 20 - y
Now we substitute this value of x into the second equation:
0.25(20 - y) + 0.05y = 4.8
5 - 0.25y + 0.05y = 4.8
Combine like terms:
-0.2y = -0.2
Divide both sides by -0.2:
y = 1
Now we know that y, the amount of the 5% orange juice, is 1 liter.
To find x, substitute the value of y back into the first equation:
x + 1 = 20
x = 20 - 1
x = 19
Therefore, you should use 19 liters of the 25% orange juice and 1 liter of the 5% orange juice to have a 20L mixture that is 24% orange juice.
Yes, you are on the right track so far. You correctly set up the system of equations:
x + y = 20 (equation 1, representing the sum of the amounts)
0.25x + 0.05y = 0.24(20) (equation 2, representing the desired percentage of orange juice)
To proceed, you need to solve this system of equations. There are multiple methods you can use, but one commonly used method is substitution. Here's how you can do that:
1. Solve equation 1 for x in terms of y:
x = 20 - y
2. Substitute this expression for x in equation 2:
0.25(20 - y) + 0.05y = 0.24(20)
3. Simplify and solve for y:
5 - 0.25y + 0.05y = 4.8
-0.2y = -0.2
y = 1
4. Substitute the value of y back into equation 1 to find x:
x + 1 = 20
x = 19
Therefore, you need 19 liters of the 25% orange juice and 1 liter of the 5% orange juice to obtain a 20-liter mixture that is 24% orange juice.
If you verify the solution by substituting these values into equation 2, you will see that it satisfies the desired percentage of orange juice.
You can also double-check your answer by dividing the amount of orange juice in the final mixture by the total volume of the mixture:
[(0.25 * 19) + (0.05 * 1)] / 20 = 0.24
This confirms that the mixture contains 24% orange juice.