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14 September, 14:11

Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer

she would pay $2,500 down and $150 each month. At another dealer, she would pay $3,000 down and $125

each month. After how many months would the total amount paid be the same for both dealers? What

would that amount be?

Lesson 2

rule 2

I need answers

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Answers (1)
  1. 14 September, 17:26
    0
    After 20 months the total amount paid would be same for both

    The amount is $5500

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - Kenya plans to make a down payment plus monthly payments in

    order to buy a motorcycle

    - There are two dealer

    # 1st : she would pay $2,500 down and $150 each month

    # 2nd : she would pay $3,000 down and $125 each month

    - We need to know after how many months the total amount paid

    would be the same for both dealers

    * Lets change the two dealer to two equations

    - Let f (x) represents the total amount of the motorcycle in x months

    ∴ f (x) = 2500 + 150 x ⇒ 1st dealer

    ∴ f (x) = 3000 + 125 x ⇒ 2nd dealer

    - Equate the two equations

    ∴ 2500 + 150 x = 3000 + 125 x

    - Subtract 125 x from both sides and 2500 from both sides

    ∴ 150 x - 125 x = 3000 - 2500

    ∴ 25 x = 500

    - Divide both sides by 25

    ∴ x = 20

    * After 20 months the total amount paid would be same for both

    - To find the amount substitute the value of x in one of the

    two equation

    ∵ f (x) = 2500 + 150 x

    ∵ x = 20

    ∴ f (x) = 2500 + 150 (20)

    ∴ f (x) = 2500 + 3000

    ∴ f (x) = 5500

    ∵ f (x) represents the total amount of the motorcycle

    * The amount is $5500
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