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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Nina and Jerry are comparing the international calling plans on their cell phones. On her plan, Nina pays just to place a call and for each minute. When Jerry makes an international call, he 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 duration? What is the cost?A call of _____ minutes would cost _____ under each plan.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Nina and Jerry are comparing the international calling plans on their cell phones. On her plan, Nina pays just to place a call and for each minute. When Jerry makes an international call, he 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 duration? What is the cost?A call of _____ minutes would cost _____ under each plan.
- Set up equations: Set up the equations based on the given information.Nina's plan: Cost = (call charge) + * durationJerry's plan: Cost = (call charge) + * durationLet's denote the duration of the call as '' and the total cost as ''.Nina's equation: Jerry's equation:
- Set cost equations: Since the cost is the same under both plans, we can set the equations equal to each other to find the duration.
- Set equal equations: Solve for 'd' by subtracting from both sides of the equation.
- Solve for duration: Subtract from both sides to isolate the term with ''.
- Subtract to isolate: Divide both sides by to solve for .
- Divide to solve: Now that we have the duration, we can find the cost for each plan.Using Nina's equation:
- Find Nina's cost: Verify the cost using Jerry's equation.
- Verify using Jerry's equation: Confirm that the cost is the same under both plans, which it is ($\(6\)), so the solution is correct.
