Inequality Word Problems

Practice writing and solving an inequality when given a word problem.

Logan's pool can hold a maximum of 3,500 gallons of water. The pool already contains 1,500 gallons of water. Logan begins to add more water at a rate of 20 gallons per minute.

To find out how many minutes, m, Logan can continue to add water without exceeding the maximum number of gallons, we can write and solve the following inequality:

\[ 1500 + 20m \leq 3500 \]

Explanation:
- Logan already has 1,500 gallons of water in the pool.
- He adds water at a rate of 20 gallons per minute.
- We multiply the rate (20 gallons per minute) by the number of minutes (m) to find out how much water Logan will add in total.
- We add this to the initial amount of water (1,500 gallons) and set it less than or equal to the maximum capacity of the pool (3,500 gallons).

Now, let's solve for m:
\[ 1500 + 20m \leq 3500 \]

Subtract 1500 from both sides:
\[ 20m \leq 2000 \]

Divide both sides by 20:
\[ m \leq 100 \]

So, Logan can continue to add water to the pool for a maximum of 100 minutes without exceeding the maximum number of gallons.

 

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