Question

Mrs. Burns has a certain number of pennies. She gives Ben 2 pennies and 1/3 of what she has left. She then gives Audrey 2 pennies and 1/3 of what is left. What is the smallest number of pennies Mrs. Burns could have started with and still have some pennies left?

Answer 1

Answer: The smallest number of pennies is 5.

Explanation:

Let initially Mrs. Burns have x pennies.

According to the question, She gives Ben 2 pennies and 1/3 of what she has left.

Thus remaining pennies = 2/3(x-2)

Again, She gives Audrey 2 pennies and 1/3 of what is left.

Then remaining pennies = 2/3(2/3(x-2)-2) = 4/9(x-2)-4/3

Since, For smallest number of pennies,

4/9(x-2)-4/3 ≥ 0

⇒
`(4(x-2)-12)/(9)\geq0`

⇒
`(4x-8-12)/(9)\geq 0`

⇒
`(4x-20)/(9)\geq 0`

⇒
`4x-20\geq 0`

⇒
`x\geq 5`

Therefore smallest number of pennies she could, is 5.