How many phone calls did she receive each evening?

Question

Over the last three evenings, Christine received a total of 120 phone calls The third evening, she received three times as many as the first evening. The first evening, she received 5 fewer calls than the second evening.

Answer 1

Let x = the number of calls received the second evening

Let x - 5 = the number of calls received the first evening

Let 3(x - 5) = the number of calls received the third evening

x + x - 5 + 3x - 15 = 120

5x - 20 = 120

5x = 140 

x = 28

x - 5 = 23

3(x - 5) = 3(23) = 69

 

 

 

Answer 2

To start this, let's let x=number of day 1 calls, y=number of day 2 calls, and z=number of day 3 calls. Since the third evening she received three times as many calls as the first evening, we can write 3x=z. Since the first evening she received five fewer than the second, we can write x=y-5. Since she received 120 total we know x+y+z=120. So now we have three equations.

 

x+y+z=120

3x=z

x=y-5

 

Since x is the common variable in the last two equations, we want to solve z and y in terms of x. The second equation is already solved in terms of z so we keep z=3x. The third equation we will rewrite as y=x+5. Plugging each of these into the first equation we get:

x+(x+5)+3x=120. Solving, we combine terms to get 5x+5=120. Thus, 5x=115 and dividing by 5 we get x=23. If x=23, then 3(23)=69=z. Furthermore, 23=y-5 so y=28.

 

Finally we have solved that she received 23 calls the first night, 28 calls the second night, and 69 calls the third night.