Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Emmett and Cooper are comparing the international calling plans on their cell phones. On his plan, Emmett pays $4 just to place a call and $1 for each minute. When Cooper makes an international call, he pays $1 to place the call and $2 for each minute. A call of a certain duration would cost exactly the same under both plans. What is the cost? What is the duration?

Answer 1

For Emmett

Let:

y1 = Total cost

x = Number of minutes

a = Cost of each minute = 1

b = Cost of place a call = 4

For Cooper:

Let:

y2 = Total cost

x = Number of minutes

c = Cost of each minute = 2

d = Cost of place a call

Therefore:

`\begin{gathered} y1=ax+b \\ y1=x+4 \\ -------- \\ y2=cx+d \\ y2=2x+1 \end{gathered}`

We find the duration and the cost of this situation solving the following equation:

`\begin{gathered} y1=y2 \\ x+4=2x+1 \\ _{\text{ }}solve_{\text{ }}for_{\text{ }}x_{}\colon \\ 2x-x=4-1 \\ x=3 \end{gathered}`

Answer:

The cost is $7 and the duration is 3 minutes.