Question

HELP ME ASAP IF U CAN!!! 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.

Answer 1

3.75 gallons of water should be added

Explanation:

Answer 2

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 (
`r`), dimensionless, is determined by the following expression:

`r = (V_(sugar))/(V_(sugar)+V_(water))` (1)

Where:

`V_(sugar)` - Volume of sugar, measured in gallons.

`V_(water)` - 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:

`r' = (V_(sugar))/(V_(sugar)+V_(water)+V')` (2)

Where
`V'` is the addition of water needed to dilute the solution, measured in gallons.

If we now that
`V_(sugar) = 3.5\,gal`,
`V_(water) = 1.5\,gal` and
`r' = 0.4`, then the quantity of additional water is:

`(3.5\,gal)/(5\,gal+V') = 0.4`

`3.5 = 0.4\cdot (5+V')`

`3.5 = 2+0.4\cdot V'`

`0.4\cdot V' = 1.5`

`V' = 3.75\,gal`

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