Question

Over the last three evenings, Raina received a total of 83 phone calls at the call center. The first evening, she received 7 more calls than the third evening. The second evening, she received 2 times as many as the third evening. How many phone calls did she receive each evening?

Answer 1

We can model this situation.

Raina received a total of 83 calls
First evening she received 7 more than the third so let x = third and since we know she received 7 more we know to add 7 to the third so (x + 7)

Second evening she received 2 times as many as the third so 2 time third, which x is the third so (2 times x) or we could say 2x

Third evening = x

So now lets solve for x and then we can find how many she received each evening.

Our Model: (x + 7) + 2x + x = 83
(x + 7) + 2x + x = 83
x + 7 + 2x  + x = 83
x + 2x  + x + 7 = 83
4x + 7 = 83
4x + 7 - 7 = 83 -7
4x = 76
4x / 4 = 76 / 4
x = 19 

First evening:
19 + 7 = 26 calls
Second evening
2 times 19 = 38
Third evening
19

Check our answer:
26 + 38 + 19 = 83