Problem Solving

[Guest]

3 people had a bag of apples. While two of them were sleeping one of them ate 1/3 of the apples. Later a second person ate 1/3 of those remaining apples. Finally the third person ate 1/3 of those remaining apples, leaving 8 apples in the bag. How many apples were in the bag originally?

 

[stapel]

Is this all the information? Did they not give you the amount left over after the third person ate some?

Eliz.

 

[stapel]

3 people had a bag of apples. While two of them were sleeping one of them ate 1/3 of the apples. Later a second person ate 1/3 of those remaining apples. Finally the third person ate 1/3 of those remaining apples, leaving 8 apples in the bag. How many apples were in the bag originally?

You are given that eight were left after eating one-third of the remaining apples. Then "8" is two-thirds of what had remained. What number is 8 two-thirds of? (Hint: Divide eight into two parts. Add one part to the two parts, for three parts. The 8 was two-thirds of the three parts, and the sum of the three parts was the number that 8 was two-thirds of.)

Follow backwards through the steps, using this logic, until you get back to the original amount.

Eliz.

 

[soroban]

Hello, Brittany Bache!

3 people had a bag of apples.
While two of them were sleeping one of them ate 1/3 of the apples.
Later a second person ate 1/3 of those remaining apples.
Finally the third person ate 1/3 of those remaining apples, leaving 8 apples in the bag.
How many apples were in the bag originally?

Let \(\displaystyle N\) = number of apples in the bag originally.

After the first person ate, there were \(\displaystyle \frac{2}{3}N\)apples left.

After the second person ate, there were \(\displaystyle \frac{2}{3}\,\times\,\frac{2}{3}N \,=\,\frac{4}{9}N\)apples left.

After the third person ate, there were \(\displaystyle \frac{2}{3}\,\times\,\frac{4}{9}N\,= \,\frac{8}{27}N\)apples left.

. . But we are told that there were 8 apples left.

There is our equation! . . . . \(\displaystyle \frac{8}{27}N = 8\qquad\Rightarrow\qquad N = 27\)