Answer:
After 20 months the total amount paid would be same for both
The amount is $5500
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