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?

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