Respuesta :

Answer:

400 gallons of 90% antifreeze solution  must be mixed with 80 gallons of 30% antifreeze to get a mixture that is 80% antifreeze.

Step-by-step explanation:

Let x be the unknown gallons of 90% antifreeze solution

Now we can write an equation to express the combining of the two solutions of antifreeze to give the desired solution of antifreeze

   0.90x + 0.30(80) = 0.80(x + 80)

To solve the above equation for x :

0.90x + 0.30(80) = 0.80(x + 80)

   0.90x + 24 = 0.80x + 64

   0.90x - 0.80x = 64-24

              0.10x = 40

               [tex]x =\frac{40}{0.10}[/tex]

                   ∴ x = 400

 ∴ 400 gallons of 90% antifreeze solution  must be mixed with 80 gallons of 30% antifreeze to get a mixture that is 80% antifreeze