Answer :
Below is a step-by-step explanation:
1. We are given the equation
[tex]$$3500 - 25x = 3000 - 15.$$[/tex]
2. This equation models the following situation:
- Pool A: It started with [tex]$3500$[/tex] liters of water and is losing water at a rate of [tex]$25$[/tex] liters per minute.
- Pool B: It started with [tex]$3000$[/tex] liters of water and had [tex]$15$[/tex] liters removed (a one-time removal). After the removal, the amount of water in Pool B is
[tex]$$3000 - 15.$$[/tex]
- The equation sets the condition that after [tex]$x$[/tex] minutes, the amount of water left in Pool A will be equal to the amount of water remaining in Pool B.
3. First, calculate the amount of water in Pool B after the removal:
[tex]$$3000 - 15 = 2985.$$[/tex]
So, Pool B has [tex]$2985$[/tex] liters remaining.
4. Now, rewrite the equation with this value:
[tex]$$3500 - 25x = 2985.$$[/tex]
5. To solve for [tex]$x$[/tex], subtract [tex]$3500$[/tex] from both sides:
[tex]$$-25x = 2985 - 3500.$$[/tex]
6. Compute the right-hand side:
[tex]$$2985 - 3500 = -515,$$[/tex]
so
[tex]$$-25x = -515.$$[/tex]
7. Divide both sides by [tex]$-25$[/tex] to isolate [tex]$x$[/tex]:
[tex]$$x = \frac{-515}{-25} = \frac{515}{25}.$$[/tex]
8. Finally, compute the value:
[tex]$$x = 20.6.$$[/tex]
Thus, after [tex]$20.6$[/tex] minutes, the amount of water in Pool A will be equal to the water remaining in Pool B.
1. We are given the equation
[tex]$$3500 - 25x = 3000 - 15.$$[/tex]
2. This equation models the following situation:
- Pool A: It started with [tex]$3500$[/tex] liters of water and is losing water at a rate of [tex]$25$[/tex] liters per minute.
- Pool B: It started with [tex]$3000$[/tex] liters of water and had [tex]$15$[/tex] liters removed (a one-time removal). After the removal, the amount of water in Pool B is
[tex]$$3000 - 15.$$[/tex]
- The equation sets the condition that after [tex]$x$[/tex] minutes, the amount of water left in Pool A will be equal to the amount of water remaining in Pool B.
3. First, calculate the amount of water in Pool B after the removal:
[tex]$$3000 - 15 = 2985.$$[/tex]
So, Pool B has [tex]$2985$[/tex] liters remaining.
4. Now, rewrite the equation with this value:
[tex]$$3500 - 25x = 2985.$$[/tex]
5. To solve for [tex]$x$[/tex], subtract [tex]$3500$[/tex] from both sides:
[tex]$$-25x = 2985 - 3500.$$[/tex]
6. Compute the right-hand side:
[tex]$$2985 - 3500 = -515,$$[/tex]
so
[tex]$$-25x = -515.$$[/tex]
7. Divide both sides by [tex]$-25$[/tex] to isolate [tex]$x$[/tex]:
[tex]$$x = \frac{-515}{-25} = \frac{515}{25}.$$[/tex]
8. Finally, compute the value:
[tex]$$x = 20.6.$$[/tex]
Thus, after [tex]$20.6$[/tex] minutes, the amount of water in Pool A will be equal to the water remaining in Pool B.
