one canned juice drink is 30% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 20L that is 15% orange juice?
To solve this problem, we can use a strategy called the "mixture problem" or "allegation method."
Let's denote the amount of the first canned juice (30% orange juice) as x liters and the amount of the second canned juice (10% orange juice) as (20 - x) liters (since the total liquid required is 20L).
Now, let's set up the equation based on the amount of orange juice in each type of drink:
For the first canned juice:
Orange juice in the first drink = 30% of x liters = (30/100) * x liters
For the second canned juice:
Orange juice in the second drink = 10% of (20 - x) liters = (10/100) * (20 - x) liters
To find the total amount of orange juice in the mixture, we add the orange juice from the first and second drinks:
Total orange juice = (30/100) * x + (10/100) * (20 - x)
According to the problem, this total orange juice should be 15% of the total mixture, which is 15% of 20L:
(15/100) * 20 = (30/100) * x + (10/100) * (20 - x)
Now, let's solve this equation to find the value of x:
3 * 20 = 3x + (20 - x)
60 = 3x + 20 - x
Collecting like terms on the right side:
60 - 20 = 3x - x
40 = 2x
Dividing both sides by 2:
x = 40/2
x = 20
Therefore, in order to get 20L of juice mixture that is 15% orange juice, you would need to mix 20 liters of the first juice (30% orange juice) with 0 liters of the second juice (10% orange juice).
if x is 30% then the rest (20-x) is 10%. So,
.30x + .10(20-x) = .15(20)
x = 5
So, 5L of 30% and 15L of 10%
Note how 15% is 3/4 of the way from 30% to 10%, so 3/4 of the mix is the 10% kind.