Chapter 1.5, Problem 23STP

To determine

How many cherries were in the bowl before Isabelle arrived.

Answer to Problem 23STP

  $32\text{cherries}$

Explanation of Solution

Given:

Isabelle took half of the cherries from a bowl. Then roberto took half of the remaining cherries, finally malia took 3 cherries from the bowl, this left 5 cherries in the bowl.

In order to find how many cherries were in the bowl before Isabelle arrived, first let there be x number of cherries in the bowl before Isabelle arrived, then Isabelle took half of the cherries from a bowl, that is x/2, then roberto took half of the remaining cherries, that is x/4, then malia took 3 cherries from the bowl, and 5 cherries are left in the bowl, now adding them is equal to x and solving it a shown below:

  $\begin{array}{l}\frac{x}{2}+\frac{x}{4}+3+5=x\\ \frac{2x+x}{4}+8=x\\ \frac{3x}{4}+8-8=x-8\\ \frac{3x}{4}=x-8\\ \frac{3x}{4}-x=x-x-8\\ \frac{3x-4x}{4}=-8\\ \frac{-x}{4}=-8\\ \frac{-x}{4}\times -4=-8\times -4\\ x=32\end{array}$

So, there are 32 cherries in the bowl before Isabelle arrived.