Zuhalie needs to rent a racing bike. She is choosing between two rental options. Option A is $50 per month with a $200 down payment. Option B is $25 per month with a down payment of $500. How many months would Zuhalie have to rent the bikes in order for the total cost of each option to be the same?

Answer: Zuhalie will have to rent the bikes for 12 months in order for the total cost of each option to become the same.

Step-by-step explanation:

In the first option ... call it option A, Zuhalie will need to pay an immediate down payment of $200 and then pay $50 each month. Now, let us use "m" to represent the number of months she will pay this $50 before the total cost of option A equals the cost of the alternative.

Again, she also has the option (say, option B) of making a down payment of $500 and then continue making $25 monthly payment. Let us also use "m" to represent the number of months she will pay this $25 before the cost of option B will equal the cost of option A.

So the total cost of option A for the period it equals the cost of option B is 200 + 50x and the total cost of option B for the period it equals the cost of option A is 500 + 25x. This will now lead us to the equation:

200 + 50x = 500 + 25x

50x - 25x = 500 - 200

25x = 300

x = 300/25

x = 12 months.

Therefore the total number of months that it will take before the cost of option A equals option B is 12 months.

Step-by-step explanation:

Given:

Option a:

Down payment, Da = $200

Monthly fee, Ma = $50

Option B:

Down payment, Db = $500

Monthly fee, Mb = $25

Monthly fee, M = payment, P/number of months, n

Total cost, Pc = down payment, D + payment, P

Equating both options we have:

500 + 25 * n = 200 + 50 * n

500 + 25n = 200 + 50 n

25n = 300

n = 300/25

= 12 months

At 12 months, both payment options will be the same.