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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Noah and Jane are comparing the international calling plans on their cell phones. On his plan, Noah pays just to place a call and for each minute. When Jane makes an international call, she pays to place the call and 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?Under each plan, a call would cost _____ if it were _____ minutes in duration.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Noah and Jane are comparing the international calling plans on their cell phones. On his plan, Noah pays just to place a call and for each minute. When Jane makes an international call, she pays to place the call and 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?Under each plan, a call would cost _____ if it were _____ minutes in duration.
- Define Variables: Let's define the variables: let be the duration of the call in minutes, and let be the total cost of the call for both plans.Noah's plan: (flat fee) + (per minute) (minutes) = Jane's plan: (flat fee) + (per minute) (minutes) = Now we can write the system of equations:
- Write Equations: Since the cost is the same for both plans, we can set the two equations equal to each other to find the duration of the call:
- Set Equations Equal: Now we will solve for by subtracting from both sides:
- Solve for x: Next, we subtract from both sides to isolate the term with :
- Substitute : Now we divide both sides by to solve for :So the duration of the call is minute.
- Find Cost: We can now substitute into either of the original equations to find the cost . Let's use Noah's plan:So the cost of the call is .
