College algebra

Question

You buy 8 gallons of orange juice that is 35% concentrated and you want to mix in some other fruit that is 80% concentrated so that the final solution is 50% concentrated, how many gallons (of the 80% concentration) do you need to add?

Answer 1

35(8) + 80X = 50(8+X)

280 + 80X = 400 + 50X

30X = 120

X = 4 gallons of 80% concentrated fruit

You want to mix 35 and 80 to get 50. 50 is 30 from 80 but 15 from 35. It's twice as close to 35 as 80, so you need half as much 80% to get to 50% half of 8 is 4 gallons