Question

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

Answer 1

5 liters of water

Answer 2

5 liters of water.

Explanation:

Let
`y` be the liters of water that must be added to 15 liters of 40% sugar syrup.

Initially, we have
`0.4(15)=6` liters of sugar syrup, and since adding water does not add any new syrup, the amount of sugar syrup must be the same after the water has been added. After the water has been added, 30% of the solution is sugar syrup, or

`Sugar\:syrup =0.3(15+y)`

And since this must equal the amount of syrup we had before:

`0.3(15+y)=0.4(15)`

`4.5+0.3y=6`

`0.3y=1.5`

`\boxed{y=5}`

Thus, 5 liters of water must be added to obtain 30% sugar syrup.