Question

i can solve real - world inequalities.

1. sam can join a gym for $25.00 per month or for a flat rate of $500.00. what is the minimum number of months sam would have to be a gym member to make the flat rate a better choice?
2. a lake is rising at a rate of 4 inches per hour. if the lake rises more than 36 inches, then it will cause flood damage. how long can the lake rise at this rate without causing flood damage?

Explanation:

Step1: Define variable for months

Let $m$ = number of months.

Step2: Set up cost inequality

We want flat rate < monthly rate:
$500 < 25m$

Step3: Solve for $m$

Divide both sides by 25:
$\frac{500}{25} < m$
$20 < m$
Since $m$ must be a whole number, the minimum $m$ is 21.

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Step1: Define variable for time

Let $t$ = time in hours.

Step2: Set up height inequality

Rise ≤ 36 inches:
$4t \leq 36$

Step3: Solve for $t$

Divide both sides by 4:
$t \leq \frac{36}{4}$
$t \leq 9$

Answer:

1. 21 months
2. At most 9 hours