Question

Over the last three evenings, Jane received a total of 80 phone calls at the call center. The second evening, she received 2 times as many calls as the thirdevening. The first evening, she received 8 fewer calls than the third evening. calls did she receive each evening?

Answer 1

This is a question on word problem.

We develop each statement into mathematical expressions.

Let the following letters represent the calls received for three evenings

`\begin{gathered} a=\text{first evening} \\ b=\text{second evening} \\ c=\text{third evening} \end{gathered}`

The statements are written as equations below;

`\begin{gathered} \text{Jane received a total of 80 phone calls. This means;} \\ a+b+c=80\ldots\ldots.\ldots..\ldots\ldots\ldots\ldots.\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ \\ The\text{ second evening, she received 2 times as many calls as the third evening. This means;} \\ b=2c\ldots\ldots\ldots\ldots\ldots\ldots\ldots.\ldots.\text{.}(2) \\ \\ \text{The first evening, she received 8 fewer calls than the third evening. This means;} \\ a=c-8\ldots\ldots\ldots\ldots\ldots.\ldots\ldots(3) \end{gathered}`

Substituting equations (3) and (2) in equation (1);

`\begin{gathered} a+b+c=80 \\ (c-8)+2c+c=80 \\ \text{Collecting the like terms;} \\ c+2c+c=80+8 \\ 4c=88 \\ \text{Dividing both sides by 4 to get c;} \\ c=(88)/(4) \\ c=22 \end{gathered}`

Substituting the value of c in equations (2) and (3) to get b and a respectively,

`\begin{gathered} b=2c \\ b=2(22) \\ b=2*22 \\ b=44 \\ \\ \\ a=c-8 \\ a=22-8 \\ a=14 \end{gathered}`

Therefore,

First evening = 14 phone calls

Second evening = 44 phone calls

Third evening = 22 phone calls