End-of-Unit Project

Swimming Pool Costs in Different Recreation Centres

Different Variables Used in the Situation

Recreation Centre A: C = 5n

Recreation Centre B: C = 3n + 10


In both cases, C represents the cost of using the pool and n represents the number of visits. Recreation Centre B has a constant / fixed cost of $10 per month.

Equations

y = mx + b form


Recreation Centre A: y = 5x | Recreation Centre B: y = 3x + 10


Ax + By = C form


Recreation Centre A: 5x - y = 0 | Recreation Centre B: 3x - y = -10

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Graphic Solution

The graphic solution of this linear system would be (5, 25) as at that point the cost of the two recreation centres would be the same.


In other words, the costs of Recreation Centre A and Recreation Centre B will both be 25$ in 5 visits.

Significance of the Solution

The solution to this linear system is significant because one who swims would want to know which recreation centre is right for them. For example, a person who would go swimming once a week would choose Recreation Centre A, as it is cheaper if you go less than 5 times. But on the other hand, someone who goes swimming 2 or 3 times a week would choose Recreation Centre B, as it is cheaper if you go more than 5 times a week.

In Closing...

The cost of the two recreation centres will be the same ($25) if one visits 5 times. Recreation Centre A is cheaper if one visits less than 5 times and Recreation Centre B is cheaper if one visits more than 5 times.