Question

Al saves pennies. He agreed to give 3/7 of his pennies to Bev if she would give 3/7 of what she got from Al to Carl and if Carl in turn would give 3/7 of what he got from Bev to Dani.​ Bev, Carl, and Dani agreed and Dani received 216 pennies. How many pennies did Al have​ initially?

Answer 1

2744 pennies.

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
`(3)/(7)x`.

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
`(3)/(7)x\cdot (3)/(7)=(9)/(49)x`.

Further, Carl gave 3/7 of what he got from Bev to Dani, so number of pennies that Dani will get would be
`(9)/(49)x\cdot (3)/(7)=(27)/(343)x`.

We are also told that Dani received 216 pennies. Now, we will equate 216 to
`(27)/(343)x` and solve for x as shown below:

`(27x)/(343)=216`

`(27x)/(343)*343=216*343`

`27x=74088`

`(27x)/(27)=(74088)/(27)`

`x=2744`

Therefore, Al have 2744 pennies initially.