https://file.aiquickdraw.com/mathbot/file/17257865233129p7iz8aq.jpg

Let's analyze the image and solve the questions provided in it. Here's a breakdown of each question:

1. **Calvin sold a motorcycle which originally cost him $5000. He made a loss of 15% when he sold it.**
   - **(a) What was the selling price?**
   - **(b) What fraction of the cost price was the selling price?**

2. **In a school bus, the ratio of girls to boys is 2:3. If the next stop some girls get off so that the ratio of girls to boys is now 4:5, if there are now 20 girls on the bus, how many girls got off the bus?**

3. **Dan’s Discount Sale: Everything must go! All marked prices reduced in the ratio 6:5.**
   - **(a) Dan's discount sale has a game for $60. What was the marked price?**
   - **(b) He said, "This has been a good sale for us." What would the marked price have been?**

### Now, let's solve each question step-by-step.

#### Question 1:
(a) **Calculating the Selling Price:**

The original cost of the motorcycle is $5000, and Calvin made a loss of 15%.

\[
\text{Selling Price} = \text{Cost Price} - \left( \text{Loss Percentage} \times \text{Cost Price} \right)
\]

Substitute the values:

\[
\text{Selling Price} = 5000 - (0.15 \times 5000) = 5000 - 750 = 4250
\]

So, the selling price was **$4250**.

(b) **Fraction of the Cost Price:**

\[
\text{Fraction} = \frac{\text{Selling Price}}{\text{Cost Price}} = \frac{4250}{5000} = \frac{17}{20}
\]

So, the fraction of the cost price that the selling price represents is **17/20**.

#### Question 2:
Let's denote:
- The number of girls as $ G $ and the number of boys as $ B $.

Initially, the ratio of girls to boys is 2:3, so:

\[
\frac{G}{B} = \frac{2}{3} \implies G = \frac{2}{3}B
\]

When some girls get off, the new ratio becomes 4:5, and there are now 20 girls:

\[
\frac{G - x}{B} = \frac{4}{5}, \text{ where } x \text{ is the number of girls who got off.}
\]

Given $ G - x = 20 $:

\[
G = 20 + x
\]

Now substitute $ G = \frac{2}{3}B $ and solve for $ B $:

\[
\frac{20 + x - x}{B} = \frac{4}{5} \implies B = 25
\]

Since $ G = \frac{2}{3} \times 25 = 50 $, now solve for $ x $:

\[
x = G - 20 = 16
\]

So, **16 girls** got off the bus.

#### Question 3:
(a) **Calculating the Marked Price:**

The ratio of reduction is 6:5, so for every $6 of the original price, the new price is $5.

Let the marked price be $ M $:

\[
\frac{6}{5} \times 60 = M \implies M = 72
\]

So, the marked price was **$72**.

(b) This question is more of a statement and does not require a calculation.

### Would you like more details on any of these solutions or have any specific questions? Here are five related questions for practice:

1. What would the selling price be if Calvin sold the motorcycle with a 20% loss?
2. If the ratio of girls to boys on another bus is 5:7 and there are 35 boys, how many girls are there?
3. If the reduction ratio at Dan’s Discount Sale was 8:7, and a product is now priced at $56, what was its marked price?
4. How would the fraction of the selling price change if Calvin had made a 10% loss instead of 15%?
5. If 10 more girls get off the bus, what would be the new ratio of girls to boys?

**Tip:** Always convert ratios to fractions or decimals for easier calculations.

Calvin sold a motorcycle which originally cost him $5000. He made a loss of 15%. What was the selling price? What fraction of the cost price was the selling price? In a school bus, the ratio of girls to boys is 2:3. If the next stop some girls get off so that the ratio is now 4:5, and there are now 20 girls on the bus, how many girls got off the bus? Dan’s Discount Sale reduces prices in the ratio 6:5. A game is marked for $60. What was the original marked price?

This problem set covers how to solve a percentage loss problem, calculate the fraction of a cost price, and solve ratio problems involving a bus's passenger composition and price reductions at a sale. Detailed solutions are provided for students in Grades 7-9.

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