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%
To solve this problem, we need to set up an equation where the amount of chlorine in the pool after adding more chlorine is equal to 3.8% of the total volume of the pool:
Let x be the additional amount of chlorine needed to achieve a concentration of 3.8%.
The total volume of the pool after adding more chlorine is 3500 + x gallons.
The equation can be set up as:
0.01(3500) + x = 0.038(3500 + x)
Solving for x:
35 + x = 133 + 0.038x
0.962x = 98
x = 98 / 0.962
x ≈ 101.66
Therefore, approximately 101.66 gallons of chlorine would need to be added to the pool to increase the concentration to 3.8%.