Question

Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86. The cost of the call and the length of the call are related. How much would you spend a month if you make overseas calls twice a week?

Answer 1

Let:

x = duration of each call

y = cost of the call

Since the cost of the call and the length of the call are related. we can model the situation as a linear equation of the form:

`y=mx+b`

a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86, so:

`\begin{gathered} x=5,y=5.91 \\ so\colon \\ 5.91=5m+b \\ --------- \\ x=10,y=10.86 \\ so\colon \\ 10.86=10m+b \end{gathered}`

Let:

`\begin{gathered} 5m+b=5.91_{\text{ }}(1) \\ 10m+b=10.86_{\text{ }}(2) \end{gathered}`

Using elimination method:

`\begin{gathered} (2)-(1) \\ 10m-5m+b-b=10.86-5.91 \\ 5m=4.95 \\ m=(4.95)/(5) \\ m=0.99 \end{gathered}`

Replace the value of m into (1):

`\begin{gathered} 5(0.99)+b=5.91 \\ 4.95+b=5.91 \\ b=5.91-4.95 \\ b=0.96 \end{gathered}`

Therefore, the cost as a function of time is:

`y(x)=0.99x+0.96`