A pool contains 3500 gallons of 1% chlorine solution, which means that 1% of the liquid in the pool is actually chlorine: the rest is water. The goal is to find how many gallons of chlorine would need to be added to increase the concentration in the pool to 3.8%. Round your answer to the nearest gallon.
First, let's find out how many gallons of chlorine are currently in the pool:
3500 gallons x 1% = 35 gallons of chlorine
Next, let's find out how many gallons of total liquid are currently in the pool:
3500 gallons - 35 gallons = 3465 gallons of water
Let x be the number of gallons of chlorine needed to add to the pool to reach a concentration of 3.8%.
After adding x gallons of chlorine, the total liquid in the pool will be 3500 + x gallons.
The equation to find the concentration of chlorine after adding x gallons is:
(35 gallons + x gallons) / (3500 gallons + x gallons) = 3.8%
Solving the equation for x:
(35 + x) / (3500 + x) = 0.038
35 + x = 0.038 * (3500 + x)
35 + x = 133 + 0.038x
0.962x = 98
x = 101.87
Rounding to the nearest gallon, you would need to add 102 gallons of chlorine to increase the concentration in the pool to 3.8%.