SOLUTION: How many liters of 100% concentrated orange juice will I need to put in if I'm combining 6 liters of 30% concentrated orange juice with x liters of 100% concentrated orange juice

Question 874174: How many liters of 100% concentrated orange juice will I need to put in if I'm combining 6 liters of 30% concentrated orange juice with x liters of 100% concentrated orange juice to make it equal to 58% concentrated orange juice
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

" 6 liters of 30% concentrated orange juice" means you have 6*0.30 = 2 liters of pure juice

"x liters of 100% concentrated orange" means you have x*1 = x liters of pure juice

Put together, you have 2 + x liters of pure juice.

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In total, you really have 6+x liters of the juice/water mix. You want 58% of this juice/water mix to be pure juice. So that means

58% of total = amount of pure juice

58% of (6+x) = 2 + x

0.58(6 + x) = 2 + x

0.58(6) + 0.58(x) = 2 + x

3.48 + 0.58x = 2 + x

3.48 = 2 + x - 0.58x

3.48 - 2 = x - 0.58x

1.48 = 0.42x

0.42x = 1.48

x = 1.48/0.42

x = 3.5238095

You need to add about 3.5238095 liters of 100% concentrated orange juice.

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