Jacqueline invested her savings in shares of a new company. The company's share price dropped by $0.50 at the end of the first year, and by a further $2.75 at the end of the second year. The share price was $19.98 at the end of the second year.

**a.** Calculate the original share price (at the beginning of the first year).

Round to the nearest cent.

**b.** Calculate the percent change in the share price over the two-year period.

%

Round to two decimal places.

Let's solve the problem step by step.

### Part (a): Calculate the Original Share Price

We know:
- The share price at the end of the second year = $19.98
- The share price dropped by $0.50 at the end of the first year.
- The share price dropped by a further $2.75 at the end of the second year.

Let the original share price be $ P $.

The drop in price by the end of the first year:
\[
P - 0.50
\]
The drop in price by the end of the second year:
\[
(P - 0.50) - 2.75
\]

This gives the final price as:
\[
(P - 0.50) - 2.75 = 19.98
\]

Let's solve for $ P $:
\[
P - 0.50 - 2.75 = 19.98
\]
\[
P - 3.25 = 19.98
\]
\[
P = 19.98 + 3.25
\]
\[
P = 23.23
\]

So, the original share price at the beginning of the first year was **$23.23**.

### Part (b): Calculate the Percent Change in the Share Price

The percent change in the share price over the two-year period can be calculated using the formula:
\[
\text{Percent Change} = \left( \frac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}} \right) \times 100
\]
Substituting the values:
\[
\text{Percent Change} = \left( \frac{19.98 - 23.23}{23.23} \right) \times 100
\]
\[
\text{Percent Change} = \left( \frac{-3.25}{23.23} \right) \times 100
\]
\[
\text{Percent Change} \approx -13.99\%
\]

So, the percent change in the share price over the two-year period is approximately **-13.99%**.

Would you like more details or have any questions?

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Here are 8 related questions:

1. What would be the share price if the price increased by 5% in the third year?
2. How much did Jacqueline lose per share after two years?
3. If Jacqueline owned 100 shares, what is the total loss after two years?
4. How much would the share price be if it had dropped by $1.00 in the second year instead of $2.75?
5. Calculate the percent change if the share price dropped by $1.00 in both years.
6. What was the average yearly decrease in the share price over the two-year period?
7. If the share price had increased by $0.50 in the first year, what would be the final price after the second drop?
8. How much would the original price need to be to result in a final price of $15.00 after the same two drops?

**Tip:** Percent change can be negative, indicating a decrease in value.

Learn how to calculate the original share price and percent change in share price over a two-year period with a detailed step-by-step solution. This problem involves arithmetic calculations and percentage calculations, suitable for Grades 7-9 students.

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