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 $2 just to place a call and $4 for each minute. When Jerry makes an international call, he pays $4 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 duration? What is the cost? A call of _____ minutes would cost $_____ under each plan.

Question

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 $2 just to place a call and $4 for each minute. When Jerry makes an international call, he pays $4 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 duration? What is the cost?   A call of _____ minutes would cost $_____ under each plan.

Bytelearn · Accepted Answer

Set up equations: Set up the equations based on the given information. Nina's plan: Cost = $2 (call charge) + $4/minute * duration Jerry's plan: Cost = $4 (call charge) + $2/minute * duration Let's denote the duration of the call as 'd' and the total cost as 'C'. Nina's equation: C = 2 + 4d Jerry's equation: C = 4 + 2dSet cost equations: Since the cost is the same under both plans, we can set the equations equal to each other to find the duration. 2 + 4d = 4 + 2dSet equal equations: Solve for 'd' by subtracting 2d from both sides of the equation. 2 + 4d - 2d = 4 + 2d - 2d 2 + 2d = 4Solve for duration: Subtract 2 from both sides to isolate the term with 'd'. 2 + 2d - 2 = 4 - 2 2d = 2Subtract to isolate: Divide both sides by 2 to solve for 'd'. 2d / 2 = 2 / 2 d = 1Divide to solve: Now that we have the duration, we can find the cost for each plan. Using Nina's equation: C = 2 + 4(1) C = 2 + 4 C = 6Find Nina's cost: Verify the cost using Jerry's equation. C = 4 + 2(1) C = 4 + 2 C = 6Verify using Jerry's equation: Confirm that the cost is the same under both plans, which it is ($6), so the solution is correct.

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