Question

Over the last three evenings, Carmen received a total of 74 phone calls at the call center. The first evening, she received 6 fewer calls than the third evening. The second evening, she received 3 times as many calls as the third evening. How many phone calls did she receive each evening?

Answer 1

Let x be the amount of calls that Carmen received at the third evening.

The first evening she received 6 calls fewer than the third, so that is x-6. The second evening, she received 3 times the number of calls of the third evening. So that is 3*x. The sum of this three quantities should be 74,sinche she received 74 calls in total. So, we have the equation

`x\text{ - 6 +3x+x = 74}`

If we add all x values we get

`5x\text{ - 6 = 74}`

If we add 6 on both sides, we get

`5x\text{ = 74+6 = 80}`

Now, if we divide by 5 on both sides, we get

`x\text{ = }(80)/(5)=16`

So in the third evening she received 16 calls. The first evening she received 16-6 = 10 calls and the second evening she received 16*3 = 48 calls.