help me please!!

Question

how much pure antifreeze (100% Concentration) should be mixed with 10 quarts of a 30% antifreeze solution to raise the concentration to 50%

Answer 1

Hi Kortni,

 

I'll be happy to help you with this problem.

 

Let's begin by assigning a letter to represent our unknown:

    x = # quarts of 100% pure antifreeze solution

 

Now let's write expressions for the concentration amount of antifreeze in each antifreeze solution:

    (1.00)(x) = concentration amount in 100% solution

    (0.30)(10) = concentration amount in 30% solution

    (0.50)(x + 10) = concentration amount

                            in 50% solution

 

Next, we'll write an equation to express the mixing of these concentration amounts together to give us the final concentration amount:

    (1.00)(x) + (0.30)(10) = (0.50)(x + 10)

 

We can now solve our equation for our unknown (x):

    (1.00)(x) + (0.30)(10) = (0.50)(x + 10)

    x + 3 = 0.5x + 5

    x - 0.5x = 5 - 3

    0.5x = 2

        x = 2/0.5

        x = 4 (# quarts of 100% pure

                     antifreeze solution)

 

Finally, we can verify our answer by plugging it back in our equation to see if both sides prove equal:

    (1.00)(x) + (0.30)(10) = (0.50)(x + 10)

    (1.00)(4) + (0.30)(10) = (0.50)(4 + 10)

    4 + 3 = (0.5)(14)

          7 = 7 (both sides proven equal)

 

Since both sides are proven equal, we are confident that our answer is correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.