A long-distance phone call costs $0.55 for the first minute and $0.09 for each additional minute or portion thereof. Write an inequality representing the number of minutes a person could talk without exceeding $7.

Wouldn't that just be

9t + 55 ≤ 700

where t is time in whole minutes?

Yes that is correct.

You moved the decimal over twice for all of the numbers, and the equation would be 9t + 55= ? (=? would be < 700)
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Yes, you are correct. The inequality you provided, 9t + 55 ≤ 700, represents the number of minutes a person could talk without exceeding $7. Here's an explanation of how we arrived at this inequality:

Let's break down the problem step by step:

1. The first minute of the call costs $0.55, so we can write this as 1 * $0.55 = $0.55.

2. For each additional minute or portion thereof, the cost is $0.09. This means that for every minute beyond the first one, we add $0.09 to the cost. So, if the person talks for t - 1 minutes (i.e., t minutes excluding the first minute), the additional cost would be (t - 1) * $0.09 = $0.09t - $0.09.

3. To calculate the total cost, we sum up the cost of the first minute and the additional cost for the remaining minutes:
Total Cost = $0.55 + $0.09t - $0.09 = $0.55 + $0.09t - $0.09 = ($0.09t + $0.55).

4. The problem states that we should not exceed $7, so we can set up an inequality to represent this condition:
$0.09t + $0.55 ≤ $7.

5. To simplify this inequality, we can subtract $0.55 from both sides:
$0.09t ≤ $7 - $0.55.

6. Simplifying further, we have:
$0.09t ≤ $6.45.

7. Finally, we divide both sides by $0.09 to isolate t:
t ≤ $6.45 / $0.09.

To avoid dealing with decimals, we can express $6.45 / $0.09 as 645 / 9, which simplifies to 71.6666... (repeating). Since we are talking about time in whole minutes, we round down to the nearest whole number. Therefore, the final inequality that represents the number of minutes a person could talk without exceeding $7 is:
t ≤ 71.

So, your initial inequality, 9t + 55 ≤ 700, is accurate and represents the same information in a slightly different form.