Let x be the amount of 90% antifreeze.
After mixing we'll have a total of 70+x gallons.
The amount of "pure" antifreeze is 0.10(70) + 0.90x
We want the concentration to be 80%
[tex] 0.80 =\dfrac{ 0.10(70) + 0.90x}{70 + x}[/tex]
Let's clear the fractions and multiply both sides by 10.
[tex]8(70+x)=70 + 9x[/tex]
[tex]560 + 8x= 70 + 9x[/tex]
[tex]490= x[/tex]
Answer: 490 gallons
Check:
(.1(70)+.9(490))/(70+490) = .8, good
