One canned juice drink is 25% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 15L that is 125 orange juice?
use x L of 25% and 15-x of the 10%
(you have a typo at the end, I will assume you meant 12 %. If this is not right, then change the value on the right side of the equation below)
then
.25x + .1(15-x) = .12(15)
solve for x
21
To solve this problem, we can use a technique called "mixture problems" or "algebraic mixture problems." Let's break down the problem into smaller steps:
Step 1: Assign variables for the unknown quantities.
Let's assume that we need to mix x liters of the canned juice drink that is 25% orange juice. Similarly, we need to mix (15 - x) liters of the canned juice drink that is 10% orange juice. Here, x represents the amount of the first drink, and (15 - x) represents the amount of the second drink.
Step 2: Set up equations based on the given information.
Since we want to attain a mixture that is 15 liters with an orange juice concentration of 125%, we can set up the following equation:
0.25x + 0.10(15 - x) = 0.125(15)
Here, 0.25x represents the amount of orange juice in the first drink (25% of x liters), 0.10(15 - x) represents the amount of orange juice in the second drink (10% of (15 - x) liters), and 0.125(15) represents the amount of orange juice in the final mixture (125% of 15 liters).
Step 3: Simplify and solve the equation.
Let's solve the equation:
0.25x + 0.10(15 - x) = 0.125(15)
0.25x + 1.50 - 0.10x = 1.875
0.15x + 1.50 = 1.875
0.15x = 1.875 - 1.50
0.15x = 0.375
x = 0.375 / 0.15
x = 2.5
So, we need to mix 2.5 liters of the canned juice drink containing 25% orange juice and (15 - 2.5) = 12.5 liters of the canned juice drink containing 10% orange juice to obtain 15 liters of a mixture with 125% orange juice concentration.