Question

over the last three evenings, ivanna received a total of 78 phone calls at the call center. the third evening, she received 2 times as many calls as the first evening. the second evening, she received 10 fewer calls than the first 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:

Step1: Define variables for calls

Let $x$ = calls on first evening.
Second evening: $x - 10$
Third evening: $2x$

Step2: Set up total calls equation

Total calls: $x + (x - 10) + 2x = 78$

Step3: Simplify and solve for $x$

Combine like terms: $4x - 10 = 78$
Add 10 to both sides: $4x = 88$
Divide by 4: $x = \frac{88}{4} = 22$

Step4: Calculate calls for each evening

First evening: $x = 22$
Second evening: $22 - 10 = 12$
Third evening: $2 \times 22 = 44$

Step5: Verify total

Check: $22 + 12 + 44 = 78$ (matches given total)

Answer:

Number of phone calls the first evening: 22
Number of phone calls the second evening: 12
Number of phone calls the third evening: 44