Naomi wants to buy a new computer for​ $840. She is considering two payment plans that require weekly payments. Which plan will pay for the computer​ faster? Explain.

Question

​BUDGET: $840
Plan​ A:
​$180 down
​$60/wk payments
Plan​ B:
​$0 down
​$70/wk payments
Question content area bottom
Part 1
Plan A will pay for the computer in
  
enter your response here weeks and plan B will pay for the computer in
  
enter your response here ​weeks, so
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Answer 1

To determine how many weeks each plan will take to pay off the computer, we need to calculate the total cost of the computer after the down payment (for Plan A) and then see how many weeks it will take to pay off the remaining balance with weekly payments.

Plan A:

• Cost of Computer: $840
• Down Payment: $180
• Remaining Balance: $840 - $180 = $660
• Weekly Payment: $60

To find out how many weeks it will take to pay off the remaining balance: \[ \text{Weeks} = \frac{\text{Remaining Balance}}{\text{Weekly Payment}} = \frac{660}{60} = 11 \text{ weeks} \]

Plan B:

• Cost of Computer: $840
• Down Payment: $0
• Remaining Balance: $840
• Weekly Payment: $70

To find out how many weeks it will take to pay off the full balance: \[ \text{Weeks} = \frac{\text{Remaining Balance}}{\text{Weekly Payment}} = \frac{840}{70} = 12 \text{ weeks} \]

Summary:

• Plan A will pay for the computer in: 11 weeks
• Plan B will pay for the computer in: 12 weeks

Thus, Plan A is faster because it will take only 11 weeks compared to 12 weeks for Plan B.