To determine the equation that represents Bryan's balance after \( n \) minutes, we first need to find out how much money is deducted from his balance for each minute of usage.
We can calculate the cost per minute by examining the change in balance:
- After 1 minute: From $52 to $45, the deduction is $52 - $45 = $7.
- After 2 minutes: From $52 to $38, the deduction is $52 - $38 = $14, which is $7 for the first minute and $7 for the second minute.
- After 3 minutes: From $52 to $31, the deduction is $52 - $31 = $21, which is $7 for the first minute, $7 for the second minute, and $7 for the third minute.
From this observation, we can see that Bryan is charged $7 per minute.
Now, to form the equation for the balance after \( n \) minutes, we can express it as follows:
\[ \text{Balance} = \text{Initial Balance} - (\text{Cost per minute} \times n) \]
Substituting in the values we have:
\[ \text{Balance} = 52 - 7n \]
Therefore, the complete equation that represents the balance on the phone after \( n \) minutes is:
\[ 52-7n \]
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