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 n…

Question

asked Oct 12, 2019 175k views

1 Answer

Skone · Answer 1 · 2019-10-18T07:03:00+0000

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.