A baker needs sugar syrup that is 40% sugar. How many gallons of water should he add to 5gallons of 70% sugar syrup to make the 40% syrup
Let x be the number of gallons of water that needs to be added.
The total amount of syrup after adding water will be 5 + x gallons.
The amount of sugar in the 5 gallons of 70% syrup is 70% of 5 = 3.5 gallons.
The amount of sugar in the final mixture will be 40% of (5 + x) = 2 + 0.4x gallons.
Since the amount of sugar in the initial syrup is equal to the amount of sugar in the final mixture, we have:
3.5 = 2 + 0.4x
Subtracting 2 from both sides:
1.5 = 0.4x
Dividing by 0.4 on both sides:
x = 1.5 / 0.4 = 3.75
Therefore, the baker needs to add 3.75 gallons of water to the 5 gallons of 70% sugar syrup to make the 40% syrup.