Questions: Over the last 3 evenings, Mary received a total of 97 phone calls at the call center. The third evening, she received 2 times as many calls as the second evening. The first evening, she received 9 fewer calls than the second evening. How many phone calls did she receive each evening? Number of phone calls the first evening: Number of phone calls the second evening: Number of phone calls the third evening: Explanation Check

Solution Steps

To solve this problem, we need to set up a system of equations based on the information given. Let \( x \) be the number of calls Mary received on the second evening. Then, the first evening would have \( x - 9 \) calls, and the third evening would have \( 2x \) calls. The total number of calls over the three evenings is 97. We can set up the equation: \( (x - 9) + x + 2x = 97 \). Solving this equation will give us the number of calls for each evening.

Let \( x \) be the number of phone calls received on the second evening. According to the problem:

• First evening: \( x - 9 \)
• Second evening: \( x \)
• Third evening: \( 2x \)

The total number of calls over the three evenings is given by the equation: \[ (x - 9) + x + 2x = 97 \]

Combining the terms, we have: \[ 4x - 9 = 97 \]

Adding 9 to both sides gives: \[ 4x = 106 \] Dividing by 4 results in: \[ x = \frac{106}{4} = \frac{53}{2} \]

Now we can find the number of calls for each evening:

• First evening: \[ x - 9 = \frac{53}{2} - 9 = \frac{53}{2} - \frac{18}{2} = \frac{35}{2} \]
• Second evening: \[ x = \frac{53}{2} \]
• Third evening: \[ 2x = 2 \times \frac{53}{2} = 53 \]

Final Answer