Solving a word problem using a system of linear equations of the form y = mx + b

Question

Two pools are being filled with water. To start, the first pool contains 2500

 liters of water and the second pool contains 2204

 liters of water. Water is being added to the first pool at a rate of 24.5

 liters per minute. Water is being added to the second pool at a rate of 33.75

 liters per minute. 

Answer 1

The y intercepts are the starting point. It will be how much water is in the pool at the start for this problem. The rates provided are the slopes. So the equations would be:

y=24.5x+2500

y=33.75x+2204

If you need to find when the pools are equal, by substitution you can set the equations equal to each other an solve.

24.5x+2500=33.75x+2204 Subtract 2204 from both sides

24.5x+2500-2204=33.75x+2204-2204

24.5x+296 = 33.75x Subtract 24.5x from both sides

24.5x-24.5x+296 = 33.75x-24.5x

296=9.25x Divide both sides by 9.25

296/9.25=9.25x/9.25

x=32

At 32 minutes, the pools will have the same amount of water in them