C3] Solve by ANY method (algebraic or graphing):
To join Karate Klub, David must pay a monthly fee of $25 and an initial fee of $200. If he
chooses Kool Karate, he must pay an initial fee of only $100 but $35/month?
Let's represent the total cost to join Karate Klub as K, and the total cost to join Kool Karate as KK.
For Karate Klub:
K = $25 (monthly fee) + $200 (initial fee)
For Kool Karate:
KK = $35 (monthly fee) + $100 (initial fee)
Now, we can compare the two options to determine when the costs are equal:
25 + 200 = 35 + 100
225 = 135
This equation is not true, which means the costs are not equal. Therefore, there is no solution to this equation and joining Karate Klub is more expensive in the long run.
To solve this problem, we need to find the point at which the total cost of joining each club is the same.
Let's represent the total cost as a function of the number of months, x.
For joining Karate Klub, the total cost, C1, can be written as:
C1 = 200 + 25x
For joining Kool Karate, the total cost, C2, can be written as:
C2 = 100 + 35x
To find the point of intersection, we set C1 equal to C2 and solve for x:
200 + 25x = 100 + 35x
Simplifying the equation, we get:
10x = 100
Dividing both sides by 10, we find:
x = 10
Therefore, the two clubs have the same total cost after 10 months.
To find the total cost after 10 months, we can substitute x = 10 into either equation:
For Karate Klub (C1), the total cost after 10 months is:
C1 = 200 + 25(10) = 200 + 250 = $450
For Kool Karate (C2), the total cost after 10 months is:
C2 = 100 + 35(10) = 100 + 350 = $450
So, after 10 months, both clubs would have the same total cost of $450.
To solve this problem, we can use algebraic methods. Let's set up an equation to represent the total cost for each option.
For joining Karate Klub, the equation would be:
Total cost = monthly fee + initial fee
Total cost = $25 + $200
Total cost = $225
For joining Kool Karate, the equation would be:
Total cost = monthly fee + initial fee
Total cost = $35/month * number of months + $100
Since we want to compare the costs of the two options, we can set them equal to each other and solve for the number of months it takes for both options to have the same total cost.
$225 = $35/month * number of months + $100
Now, let's solve for the number of months.
$225 - $100 = $35/month * number of months
$125 = $35/month * number of months
To eliminate the fraction, we can divide both sides by $35/month:
$125 / $35/month = number of months
Simplifying the left side:
$3.57/month = number of months
Rounding up, we can conclude that it would take approximately 4 months for both options to have the same total cost.
So, to compare the costs of the two options, if David plans to practice karate for less than 4 months, it would be more cost-effective for him to choose Kool Karate. However, if he plans to practice karate for 4 months or more, Karate Klub would be the more affordable option.