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

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