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Latrell works for a company that manufactures liquid dyes for clothing. He currently wants to mix up some -concentrated pink dye. He has liters of -concentrated pink dye, as well as plenty of -concentrated pink dye. How many liters of the -concentrated pink dye will Latrell need to add to the -concentrated pink dye to make a batch with a concentration of ? Write your answer as a whole number or as a decimal rounded to the nearest tenth. liters
Full solution
Q. Latrell works for a company that manufactures liquid dyes for clothing. He currently wants to mix up some -concentrated pink dye. He has liters of -concentrated pink dye, as well as plenty of -concentrated pink dye. How many liters of the -concentrated pink dye will Latrell need to add to the -concentrated pink dye to make a batch with a concentration of ? Write your answer as a whole number or as a decimal rounded to the nearest tenth. liters
- Denote amount of dye: Let's denote the amount of -concentrated pink dye that needs to be added as liters.
- Calculate pure dye in % solution: Calculate the amount of pure dye in the liters of -concentrated pink dye. liters
- Calculate pure dye in liters: Calculate the amount of pure dye in the liters of -concentrated pink dye. liters
- Total pure dye in final mixture: The total amount of pure dye in the final mixture should be equal to the sum of the pure dye from both solutions, which should be of the total volume ( liters + liters).
- Set up equation: Set up the equation based on the total amount of pure dye in the final mixture.
- Distribute .: Distribute the on the right side of the equation.
- Simplify equation: Simplify the equation by combining like terms.
- Subtract : Subtract from both sides of the equation to get all the x terms on one side.
- Subtract .: Subtract from both sides of the equation to isolate the term.
- Calculate value of x: Calculate the value of .
