Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Janelle and Duncan are comparing the international calling plans on their cell phones. On her plan, Janelle pays $1 just to place a call and $5 for each minute. When Duncan makes an international call, he pays $5 to place the call and $1 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.  Janelle and Duncan are comparing the international calling plans on their cell phones. On her plan, Janelle pays $1 just to place a call and $5 for each minute. When Duncan makes an international call, he pays $5 to place the call and $1 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

Define Variables: Let's define the variables: let x be the duration of the call in minutes, and let y be the total cost of the call for each plan. We need to set up two equations based on the information given for Janelle and Duncan's calling plans. Janelle's plan: Cost = $1 (to place a call) + $5/minute * x (duration) Duncan's plan: Cost = $5 (to place a call) + $1/minute * x (duration) Since the cost is the same for both plans, we can equate the two expressions for cost.Set Up Equations: Now we write the system of equations based on the above information: For Janelle: y = 1 + 5x For Duncan: y = 5 + x Since the costs are the same, we can set the two equations equal to each other: 1 + 5x = 5 + xWrite System of Equations: Next, we solve for x by subtracting x from both sides of the equation: 1 + 5x - x = 5 + x - x 1 + 4x = 5Solve for x: Now, we subtract 1 from both sides to isolate the term with x: 1 + 4x - 1 = 5 - 1 4x = 4Substitute x to Find y: To find the value of x, we divide both sides by 4: 4x / 4 = 4 / 4 x = 1Now that we have the duration (x), we can find the cost (y) by substituting x back into either of the original equations. Let's use Janelle's equation: y = 1 + 5x y = 1 + 5(1) y = 1 + 5 y = 6

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