Question

Over the last three evenings, Kira received a total of 54 phone calls at the call center. The first evening, she received 10 fewer calls than the second evening. The third evening, she received 2 times as many calls as the second evening. How many phone calls did she receive each evening?

Answer 1

Let x, y, and z be the number of calls Kira received during the first, second, and third day, respectively. Therefore, the equations are

$\begin{gathered} x+y+z=54 \\ x=y-10 \\ z=2y \end{gathered}$

Solve the system of equations as shown below

$\begin{gathered} \Rightarrow x+y+z=x+(x+10)+2(x+10)=4x+30 \\ \Rightarrow4x+30=54 \\ \Rightarrow4x=24 \\ \Rightarrow x=6 \end{gathered}$

Use the value of x to find y and z,

$\begin{gathered} x=6 \\ \Rightarrow6=y-10\Rightarrow y=16 \\ and \\ z=2y=2*16=32 \end{gathered}$

Therefore, the answers are:

First evening: 6 calls

Second evening: 16 calls

Third evening: 32 calls