To find the selling price (S) and the markup (M), we can use the given equations and information.

Given:

• Cost (C) = 5,500
• Markup rate based on selling price = 15% or 0.15

Equations:

1. $M = 0.15S$ (Markup is 15% of the selling price)
2. $S = C + M$ (Selling price is the sum of cost and markup)

Steps to Solve:

1. Substitute the value of $M$ from equation 1 into equation 2:

$S = 5500 + 0.15S$

2. To solve for $S$, subtract $0.15S$ from both sides:

$S - 0.15S = 5500$

3. Combine like terms:

$0.85S = 5500$

4. Solve for $S$:

$S = \frac{5500}{0.85}$

$S \approx 6,470.59$

5. Now, calculate the markup $M$ using the value of $S$:

$M = 0.15 \times 6470.59 \approx 970.59$

Final Answers:

• Selling Price (S): Approximately P6,470.59
• Markup (M): Approximately P970.59

Would you like more details, or do you have any questions?

Here are some related questions:

1. How would the markup change if the rate was 20% instead of 15%?
2. What is the percentage markup based on the cost price?
3. How would you calculate the selling price if the markup was based on cost instead of the selling price?
4. What would happen to the selling price if the cost increased by 10%?
5. How do you determine the cost if you only know the selling price and the markup rate?

Tip: Always check whether the markup rate is based on cost or selling price, as this affects your calculations.