Represent algebraically: If b baseball cards were divided equally is total number of cards is 150
Solution:
Given that, if “b” baseball cards were divided equally among 3 people, each person would receive 25 cards less than if the “b” baseball cards were divided equally between 2 people.
We have to represent it in algebraic form.
Now, number of cards per each person when divided among 3 = number of cards per each person when divided among 2 – 25
[tex]\frac{\text { total of b cards }}{3 \text { persons }}=\frac{\text { total of b cards }}{2 \text { persons }}-25[/tex]
[tex]\begin{array}{l}{\rightarrow \frac{b}{3}=\frac{b}{2}-25} \\\\ {\rightarrow \frac{b}{3}=\frac{b-2 \times 25}{2}} \\\\ {\rightarrow \frac{b}{3}=\frac{b-50}{2}} \\\\ {\rightarrow 2 \mathrm{b}=3(\mathrm{b}-50)} \\\\ {\rightarrow 2 \mathrm{b}=3 \mathrm{b}-150} \\\\ {\rightarrow 3 \mathrm{b}-2 \mathrm{b}=150} \\\\ {\rightarrow \mathrm{b}=150}\end{array}[/tex]
Hence, total number of cards are 150
