Question

How many liters of water must be added to 15 liters of 40 % sugar syrup to obtain 30 % sugar syrup?

Answer 1

5 L of water should be added

Explanation:

Let x L is the amount of water needed to be added.

40% sugar syrup:

Amount of syrup = 15 L

Amount of sugar L

30% sugar syrup:

Amount of syrup = 15 + x L

Amount of sugar L

Amounts of sugar are the same (we didn't add sugar, only water), then

Answer 2

5 L of water should be added

Explanation:

Let x L is the amount of water needed to be added.

40% sugar syrup:

Amount of syrup = 15 L

Amount of sugar
`=15\cdot 0.4=6` L

30% sugar syrup:

Amount of syrup = 15 + x L

Amount of sugar
`=(15+x)\cdot 0.3` L

Amounts of sugar are the same (we didn't add sugar, only water), then

`0.3(15+x)=6\\ \\3(15+x)=60\\ \\45+3x=60\\ \\3x=60-45\\ \\3x=15\\ \\x=5\ L`