To determine how many shares of stock ABC Becka will own at the end of the year, let's break down her investments for each quarter and calculate the shares she buys in each one.
1. First Quarter (Q1):
- Investment: \[tex]$300
- Stock price at the end of Q1: \$[/tex]25 per share
[tex]\[
\text{Number of shares bought} = \frac{300}{25} = 12 \text{ shares}
\][/tex]
2. Second Quarter (Q2):
- Investment: \[tex]$300
- Stock price at the end of Q2: \$[/tex]26 per share
[tex]\[
\text{Number of shares bought} = \frac{300}{26} \approx 11.538 \text{ shares}
\][/tex]
3. Third Quarter (Q3):
- Investment: \[tex]$300
- Stock price at the end of Q3: \$[/tex]23 per share
[tex]\[
\text{Number of shares bought} = \frac{300}{23} \approx 13.043 \text{ shares}
\][/tex]
4. Fourth Quarter (Q4):
- Investment: \[tex]$300
- Stock price at the end of Q4: \$[/tex]28 per share
[tex]\[
\text{Number of shares bought} = \frac{300}{28} \approx 10.714 \text{ shares}
\][/tex]
Next, we sum up all the shares bought over the four quarters:
[tex]\[
\text{Total shares} = 12 \text{ shares} + 11.538 \text{ shares} + 13.043 \text{ shares} + 10.714 \text{ shares} \approx 47.295 \text{ shares}
\][/tex]
Since shares cannot be in fractions when rounding to the nearest whole number:
[tex]\[
\text{Total shares} \approx 47 \text{ shares}
\][/tex]
Thus, Becka will own a total of [tex]\( \boxed{47} \)[/tex] shares of stock ABC at the end of the year.
