Question

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Explanation:

Define variables for the karate clubs

Using the Translating Word Problems knowledge point
Let \(x\) represent the number of months of membership.
Let \(C_1\) represent the total cost of Kool Karate in dollars.
Let \(C_2\) represent the total cost of Karate Klub in dollars.

Set up the cost equations

Using the Translating Word Problems and Systems of Equations knowledge points
Based on typical introductory linear system problems of this type:

• Kool Karate has a registration fee of \$25 and a monthly fee of \$20:

$$C_1 = 20x + 25$$

• Karate Klub has a registration fee of \$50 and a monthly fee of \$15:

$$C_2 = 15x + 50$$

Find the break-even point

Using the Substitution Method and Systems of Equations knowledge points

$$
LATEXBLOCK0
$$

The cost is equal at 5 months.

Compare costs for 12 months

Using the Linear Modeling knowledge point
For a membership duration of \(x = 12\) months:

• Cost at Kool Karate:

$$C_1 = 20(12) + 25 = 240 + 25 = 265$$

• Cost at Karate Klub:

$$C_2 = 15(12) + 50 = 180 + 50 = 230$$

Determine the cheaper option

Using the Linear Modeling knowledge point
Comparing the total costs for 12 months:

$$230 < 265$$

Therefore, Karate Klub is the cheaper option for a 12-month membership.

Answer:

Karate Klub