Joyce mother buys some shares of Company A on Day 0. On Day 7, the share price of Company A is $4.60. If she sells all her shares of Company A and buys 2000 shares at Company B on Day 7, she would receive $7400. On Day 12, the share price of Company A is $4.80 and the share price of Company B is $0.50 less than that on Day 7. If she sells all her shares of Company A and buys 5000 shares on Company B on Day 12, She would have to pay $5800. Find
(i) the number of shares of Company A Joyce mother has,
(ii) the share price of Company B on Day 12

Let's break down the problem step by step.

### Given:
1. On Day 7:
   - The share price of Company A is $4.60.
   - Joyce's mother sells all her shares of Company A and buys 2000 shares of Company B.
   - She receives $7400 after buying the shares of Company B.

2. On Day 12:
   - The share price of Company A is $4.80.
   - The share price of Company B is $0.50 less than that on Day 7.
   - She sells all her shares of Company A and buys 5000 shares of Company B.
   - She has to pay $5800.

We need to find:
1. The number of shares of Company A Joyce's mother has on Day 7.
2. The share price of Company B on Day 12.

### Step 1: Find the Share Price of Company B on Day 7
Let the share price of Company B on Day 7 be $ P_B $.

When she buys 2000 shares of Company B on Day 7, she uses the money obtained from selling her shares of Company A. So:
\[
\text{Total money from selling shares of Company A} - 2000 \times P_B = 7400
\]
\[
\text{Total money from selling shares of Company A} = 2000 \times P_B + 7400
\]

### Step 2:

Explore a detailed financial investment analysis involving shares of Company A and Company B. Solve for the number of shares of Company A and determine the share price of Company B on Day 12 based on given financial transactions. Suitable for high school students learning about financial mathematics and investment analysis.

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