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# Solving Equations

From supply and demand to position and velocity, equations model the world around us. Equip yourself with the tools necessary to solve for x.

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?

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

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