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 18% orange juice?
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oj in x liters of 30% = .3x
oj in (20-x) liters of 10% = .1(20-x)
oj in 20 liters of 18% = .18(20)
.3x + .1(20-x) = .18(20)
.3x + 2 - .1x = 3.6
.2x = 1.6
x = 8
so, 8L of 30% + 12L of 10% = 20L of 18%
8*.3 + 12*.1 = 2.4+1.2 = 3.6 = .18*20
Let's assume that x liters of the 30% orange juice drink are mixed, and y liters of the 10% orange juice drink are mixed.
To solve the problem, we can use the equation:
0.30x + 0.10y = 0.18(20)
This equation represents the total amount of orange juice in the mixture. Now we can solve for x and y.
0.30x + 0.10y = 3.6
Multiplying both sides of the equation by 100 to remove the decimals:
30x + 10y = 360
Now we need another equation to represent the total volume:
x + y = 20
We can solve this system of equations using substitution or elimination. Let's use substitution here.
Rearrange the second equation in terms of x:
x = 20 - y
Substitute this value of x into the first equation:
30(20 - y) + 10y = 360
600 - 30y + 10y = 360
Combine like terms:
-20y = -240
Divide both sides by -20:
y = 12
Now substitute this value of y back into the second equation:
x + 12 = 20
x = 20 - 12
x = 8
Therefore, 8 liters of the 30% orange juice drink and 12 liters of the 10% orange juice drink should be mixed together to get 20 liters that is 18% orange juice.
To solve this problem, we can use the concept of mixture problems. Let's break it down step by step.
Let's assume we need to mix x liters of the first juice (30% orange juice) and y liters of the second juice (10% orange juice) to get a total of 20 liters.
Step 1: Write down the given information:
- First juice: 30% orange juice
- Second juice: 10% orange juice
- Total mixture: 20 liters
- Concentration in the mixture: 18% orange juice
Step 2: Set up the equation:
The amount of orange juice in the first juice plus the amount of orange juice in the second juice should be equal to the total amount of orange juice in the mixture.
0.30x + 0.10y = 0.18(20)
Step 3: Simplify and solve the equation:
0.30x + 0.10y = 3.6
Now, we have one equation with two variables. We need another equation to solve the system of equations.
Step 4: Set up a second equation:
The total volume of the first juice plus the total volume of the second juice should be equal to the total volume of the mixture.
x + y = 20
Now, we have a system of equations:
0.30x + 0.10y = 3.6 (Equation 1)
x + y = 20 (Equation 2)
Step 5: Solve the system of equations:
One approach to solving this system of equations is substitution. Rearrange Equation 2 to make x the subject:
x = 20 - y
Substitute this value of x into Equation 1:
0.30(20 - y) + 0.10y = 3.6
Simplify and solve for y:
6 - 0.30y + 0.10y = 3.6
-0.20y = 3.6 - 6
-0.20y = -2.4
Divide both sides by -0.20:
y = -2.4 / -0.20
y = 12
Now, we have found that y = 12 liters, which is the amount of the second juice.
To find the amount of the first juice (x), substitute the value of y back into Equation 2:
x = 20 - y
x = 20 - 12
x = 8
Therefore, you should mix 8 liters of the first juice (30% orange juice) and 12 liters of the second juice (10% orange juice) to obtain a 20-liter mixture with an 18% orange juice concentration.