One canned juice is 20% orange juice: another is 10% orange juice. How many liters of each should be mixed together in order to get 10L that is 13% orange juice.How many liters of the 20%?
How many liters of the 10%?
let the number of litres of the 10% kind be x
let the number of litres of the 20% kind by 10-x
solve
.1x + .2(10-x) = .13(10)
I still don't understand?
To find out how many liters of each juice should be mixed together, we can set up a system of equations.
Let's say x represents the number of liters of the 20% orange juice and y represents the number of liters of the 10% orange juice.
First, let's figure out the equation for the amount of orange juice in the mixture. Since we want a total of 10 liters of juice, the equation for the orange juice content is:
0.20x + 0.10y = 0.13 * 10
Simplifying this equation gives us:
0.20x + 0.10y = 1.3
Next, let's set up the equation for the total volume of the mixture. Since we want a total of 10 liters, the equation for the total volume is:
x + y = 10
Now we have a system of two equations:
0.20x + 0.10y = 1.3
x + y = 10
To solve this system, we can use the method of substitution or elimination. Here, we will use the method of substitution.
Solve the second equation for x: x = 10 - y
Now substitute this value for x in the first equation:
0.20(10 - y) + 0.10y = 1.3
Simplify this equation:
2 - 0.20y + 0.10y = 1.3
-0.10y = 1.3 - 2
-0.10y = -0.7
Divide both sides by -0.10:
y = -0.7 / -0.10
y = 7
Now we know that y, which represents the number of liters of the 10% orange juice, is equal to 7.
To find the number of liters of the 20% orange juice (x), substitute the value of y back into one of the original equations:
x + 7 = 10
x = 10 - 7
x = 3
Therefore, you need 3 liters of the 20% orange juice and 7 liters of the 10% orange juice to make a 10-liter mixture with a 13% orange juice content.