how many gallons of a 90% antifreeze solution must be mixed with 100 gallons of 25% antifreeze to get a mixture of 80% antifreeze?

Question

please help just need an answer

Answer 1

Hi Holly,

 

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

    x (gallons of 90% antifreeze solution)

 

Now let's write an equation to express the combining of the two solutions of antifreeze to give the desired solution of antifreeze and solve this equation for x:

    0.90x + 0.25(100) = 0.80(x + 100)

    0.90x + 25 = 0.80x + 80

    0.90x - 0.80x = 80 - 25

               0.10x = 55

                     x = 55/0.10

                     x = 550

 

Answer:  550 gallons of 90% antifreeze solution

 

We can verify that our answer for x is correct by plugging our answer into the equation and see if both sides are equal:

    0.90x + 0.25(100) = 0.80(x + 100)

    0.90(550) + 0.25(100) = 0.80(550 + 100)

    495 + 25 = 0.80(650)

            520 = 520 (both sides are equal)

 

Since both sides are equal, we are confident that we have arrived at the correct answer.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.