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Answer: 12</h3>
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Explanation:
We have 12 oz of 50% chocolate syrup, which means we have 0.50*12 = 6 oz of pure chocolate from this bottle. We add on x more ounces of pure chocolate from the second batch. So we have 6+x ounces of pure chocolate.
This is out of 12+x ounces of mixed syrup (chocolate + other stuff) overall.
The fraction (6+x)/(12+x) represents the proportion of pure chocolate to the mixed syrup batch. Set this equal to 0.75 and solve for x.
(6+x)/(12+x) = 0.75
6+x = 0.75(12+x)
6+x = 0.75(12)+0.75(x)
6+x = 9+0.75x
x-0.75x = 9-6
0.25x = 3
x = 3/0.25
x = 12
So we must add 12 ounces of pure chocolate to the mix
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We can think of this problem in terms of colored blocks.
Let's say a brown block represents a unit of pure chocolate, while a blue block is something else (say sugar or whatever other ingredients).
Currently we have 6 brown blocks (the 6 oz of pure chocolate) out of 12 blocks overall (6 brown + 6 blue).
If we add on 12 more brown blocks, then we get 6+12 = 18 brown blocks overall out of 12+12 = 24 blocks (brown+blue).
Then notice how 18/24 = 0.75 = 75% to represent the fact that 75% of the blocks are brown. So 75% of the syrup is pure chocolate.
This thought experiment is one way to help verify the answer.
