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

 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
Transcript text: 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
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Solution

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Solution Steps

To solve this problem, we need to set up a system of equations based on the information given. Let x x be the number of calls Mary received on the second evening. Then, the first evening would have x9 x - 9 calls, and the third evening would have 2x 2x calls. The total number of calls over the three evenings is 97. We can set up the equation: (x9)+x+2x=97 (x - 9) + x + 2x = 97 . Solving this equation will give us the number of calls for each evening.

Step 1: Set Up the Equations

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

  • First evening: x9 x - 9
  • Second evening: x x
  • Third evening: 2x 2x

The total number of calls over the three evenings is given by the equation: (x9)+x+2x=97 (x - 9) + x + 2x = 97

Step 2: Simplify the Equation

Combining the terms, we have: 4x9=97 4x - 9 = 97

Step 3: Solve for x x

Adding 9 to both sides gives: 4x=106 4x = 106 Dividing by 4 results in: x=1064=532 x = \frac{106}{4} = \frac{53}{2}

Step 4: Calculate Calls for Each Evening

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

  • First evening: x9=5329=532182=352 x - 9 = \frac{53}{2} - 9 = \frac{53}{2} - \frac{18}{2} = \frac{35}{2}
  • Second evening: x=532 x = \frac{53}{2}
  • Third evening: 2x=2×532=53 2x = 2 \times \frac{53}{2} = 53

Final Answer

The number of phone calls received each evening is:

  • First evening: 352 \frac{35}{2}
  • Second evening: 532 \frac{53}{2}
  • Third evening: 53 53

Thus, the final answers are: Number of phone calls the first evening: 352 \text{Number of phone calls the first evening: } \boxed{\frac{35}{2}} Number of phone calls the second evening: 532 \text{Number of phone calls the second evening: } \boxed{\frac{53}{2}} Number of phone calls the third evening: 53 \text{Number of phone calls the third evening: } \boxed{53}

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