From the question, Kala is saving money to buy a bike that costs $198. She currently has $63 and saves an additional $9 per week. We need to:

1. Write an equation that represents this situation.
2. Solve the equation to find how many weeks it will take for her to save enough money.

Step (a): Writing the equation

Let $w$ represent the number of weeks.

Kala's total savings after $w$ weeks is given by: $\text{Total savings} = 63 + 9w$

We want her total savings to be at least $198, so the equation is: $63 + 9w = 198$

Step (b): Solving the equation

To solve $63 + 9w = 198$:

1. Subtract 63 from both sides: $9w = 198 - 63$ $9w = 135$

2. Divide both sides by 9: $w = \frac{135}{9}$ $w = 15$

Final Answer:

It will take 15 weeks for Kala to save enough money to buy the bike.

Would you like additional explanation or have any questions?

Related Questions:

1. How would the solution change if the bike cost $250 instead of $198?
2. What happens if Kala saves $12 per week instead of $9?
3. What if Kala initially had $80 instead of $63?
4. How would you write the inequality if she saves for a more expensive bike and takes longer than 15 weeks?
5. Can we solve this problem graphically, and how would the graph look?

Tip:

When writing equations for word problems, carefully identify the variables and constants to set up an accurate mathematical model.