a baker needs sugar syrup that is 40% sugar how many gallons of water shoud he add to 5 gallons of 70% sugar syrup to make the 40% syrup.

The baker should add 3.75 gallon of water to 5 gallons of 70 % sugar syrup to make the 40 % syrup.

Step-by-step 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.