Algebra
# Solving Equations

Five brothers stayed in the house with their mother. One day, their mother brought home some mangos.

Alex woke up first. As he was hungry, he ate $\frac{1}{6}$ of the mangoes, and headed out.

Brian woke up next. As he was hungry, he ate $\frac{1}{5}$ of what was left, and headed out.

Charles woke up next. As he was hungry, he ate $\frac{1}{4}$ of what was left, and headed out.

Danny woke up next. As he was hungry, he ate $\frac{1}{3}$ of what was left, and headed out.

Euler woke up next. As he was hungry, he ate $\frac{1}{2}$ of what was left, and headed out.

Their mother came home and saw 3 mangoes in the basket. How many mangoes were there initially?

A teacher writes 6 consecutive integers on the blackboard.

He erases one of the integers and the sum of the remaining five integers is 2016.

What integer was erased?

True or False?

$\text{If } ac = bd \text{ and } c = d, \text{ then it is certain that } a = b.$