Answer:
The baker should add 3.75 gallon of water to 5 gallons of 70 % sugar syrup to make the 40 % syrup.
Explanation:
The percentage concentration (
), dimensionless, is determined by the following expression:
(1)
Where:
- Volume of sugar, measured in gallons.
- Volume of water, measured in gallons.
A 70 % sugar syrup means that there are 7 parts of sugar for each 10 parts of solution, that is, 7 parts of sugar and 3 parts of water. We need to add more water to dilute the solution to 40 %. Then, the new concentration must be equal to:
(2)
Where
is the addition of water needed to dilute the solution, measured in gallons.
If we now that
,
and
, then the quantity of additional water is:
The baker should add 3.75 gallon of water to 5 gallons of 70 % sugar syrup to make the 40 % syrup.