Anita is filling a pool with water. Currently, there are 60 gallons of water in the pool, and she is filling the pool at a rate of 50 gallons every 5 minutes. She wants to fill the pool with at least 200 gallons of water. Enter an inequality that represents all possible values for the number of minutes (m) that it will take to fill the pool. $$

Step-by-step explanation:

Given

Current = 60 gallons

Rate = 50 gallons per 5 minutes

Expected = At least 200 gallons

Required

Determine the inequality that represents the scenario

First, we need to calculate the unit rate

Rate = 50 gallons per 5 minutes

This implies 10 gallons per minute

The inequality is then calculated as thus:

Where m represent the number of minutes

At least 200 means greater than or equal to 200.

So, we have:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for