Answer:
2744 pennies.
Step-by-step explanation:
Let x represent the number of pennies Al have initially.
We have been given that Al agreed to give 3/7 of his pennies to Bev, so number of pennies Bev will get would be [tex]\frac{3}{7}x[/tex].
We are also told that Bev gave 3/7 of what she got from Al to Carl, so number of pennies that Carl will get would be [tex]\frac{3}{7}x\cdot \frac{3}{7}=\frac{9}{49}x[/tex].
Further, Carl gave 3/7 of what he got from Bev to Dani, so number of pennies that Dani will get would be [tex]\frac{9}{49}x\cdot \frac{3}{7}=\frac{27}{343}x[/tex].
We are also told that Dani received 216 pennies. Now, we will equate 216 to [tex]\frac{27}{343}x[/tex] and solve for x as shown below:
[tex]\frac{27x}{343}=216[/tex]
[tex]\frac{27x}{343}*343=216*343[/tex]
[tex]27x=74088[/tex]
[tex]\frac{27x}{27}=\frac{74088}{27}[/tex]
[tex]x=2744[/tex]
Therefore, Al have 2744 pennies initially.
