Question

Russ discovers at the end of the summer that his radiator antifreeze solution has dropped below the safe level. if the radiator contains 4 gallons of a 25% solution. how many gallons of pure antifreeze must he add to bring it up to a desired 50% solution (assume there is room to add antifreeze without removing any solution.)

Answer 1

To bring the radiator antifreeze solution up to a desired 50% concentration, Russ needs to add 2 gallons of pure antifreeze.

Step-by-step explanation:

To bring the radiator antifreeze solution up to a desired 50% concentration, Russ needs to calculate how much pure antifreeze he should add. Let x represent the number of gallons of pure antifreeze he needs to add. Since the radiator currently contains 4 gallons of a 25% solution, this means it contains 4 x 0.25 = 1 gallon of pure antifreeze. When Russ adds x gallons of pure antifreeze, the total volume of the solution will become 4 + x gallons. The volume of pure antifreeze in the solution will be 1 + x gallons. We can set up the following equation to solve for x:

(1 + x) / (4 + x) = 0.50

Cross-multiplying and simplifying the equation gives:

1 + x = 0.50(4 + x)

1 + x = 2 + 0.50x

0.50x - x = 2 - 1

-0.50x = 1

x = 1 / -0.50

x = -2

Since the question specifies that Russ has room to add antifreeze without removing any solution, we can ignore the negative value for x and conclude that Russ needs to add 2 gallons of pure antifreeze to bring the solution up to a desired 50% concentration.