Question

Over the last three evenings, Mary received a total of 62 phone calls at the call center. The third evening, she received two times as many calls as the first evening. The second evening, she received six fewer calls than the first evening. How many calls did she receive each evening?

a) First evening: 15 calls, Second evening: 21 calls, Third evening: 26 calls
b) First evening: 17 calls, Second evening: 11 calls, Third evening: 34 calls
c) First evening: 20 calls, Second evening: 14 calls, Third evening: 28 calls
d) First evening: 12 calls, Second evening: 18 calls, Third evening: 32 calls

Answer 1

Mary received 17 calls on the first evening, 11 calls on the second evening, and 34 calls on the third evening.

Step-by-step explanation:

Let's assign variables to represent the number of calls on each evening. Let 'x' represent the number of calls on the first evening, 'y' represent the number of calls on the second evening, and 'z' represent the number of calls on the third evening.

Based on the given information:

• The third evening, Mary received two times as many calls as the first evening: z = 2x
• The second evening, Mary received six fewer calls than the first evening: y = x - 6
• Over the last three evenings, Mary received a total of 62 phone calls: x + y + z = 62

Now we can substitute the second and third equations into the first equation to solve for the values of x, y, and z.

x + (x - 6) + 2x = 62

4x - 6 = 62

4x = 68

x = 17

Substituting this value back into the second equation, we find y = 17 - 6 = 11. And substituting the value of x into the first equation, we find z = 2(17) = 34.

Therefore, the correct answer is:

a) First evening: 17 calls, Second evening: 11 calls, Third evening: 34 calls