Question

guided practice 2. antifreeze one type of antifreeze is 40% glycol, and another type of antifreeze is 60% glycol. how much of each kind should be used to make 100 gallons of antifreeze that is 48% glycol?

Explanation:

Step1: Let the amount of 40% glycol antifreeze be $x$ gallons.

Then the amount of 60% glycol antifreeze is $(100 - x)$ gallons.

Step2: Set up an equation based on the glycol - content.

The glycol - content in the 40% solution is $0.4x$, the glycol - content in the 60% solution is $0.6(100 - x)$, and the glycol - content in the final 48% solution of 100 gallons is $0.48\times100$. So, $0.4x+0.6(100 - x)=0.48\times100$.

Step3: Expand and simplify the equation.

$0.4x + 60-0.6x=48$. Combine like - terms: $0.4x-0.6x=48 - 60$. This gives $-0.2x=-12$.

Step4: Solve for $x$.

Divide both sides of the equation by $-0.2$: $x=\frac{-12}{-0.2}=60$.

Step5: Find the amount of the other type of antifreeze.

The amount of 60% glycol antifreeze is $100 - x=100 - 60 = 40$ gallons.

Answer:

60 gallons of 40% glycol antifreeze and 40 gallons of 60% glycol antifreeze should be used.