A classmate has developed a few trick of her own. Represent the with an equation and solve it to justify the solution to her tricks.

'Think of a positive number. Multiply it by $4$ and then add $3$. Double your original number and add it to this result. Now subtract $9$. Finally divide thus result by $6$. If you tell me the result, I can tell you what number you started with.' You tell her the result is $40$. What number does she say you originally chose$?$

A classmate has developed a few trick of her own. Represent the with an equation and solve it to justify the solution to her tricks.

'Think of three consecutive positive numbers. Double the smallest one and subtract the largest one from that result. If you tell me the result, I'II tell you the numbers you started with.' You tell her the result is $70$. What number does she say you originally chose$?$

Hector tells Amaya, 'I know three consecutive positive numbers such that, if you add them, the result is one more than double the next consecutive integer.' Find the three consecutive numbers that Hector is referring to.

Amaya responds with, 'Well, I know two numbers that differ by $6$ such that, when you add them, you get $5$ times the smaller one.' Find the numbers Amaya is referring to.

Launch thinks equations are like little puzzles. He created his own number puzzle and told his friend, 'I am thinking of an integer. If I multiply my number by $2$ and subtract $4$, I get the same result as when I multiply it by $3$ and add $5$. What is my number$?$

Write down an equation that represents Launch's puzzle and find his number.

Create your own number puzzles that lead to an equation. Trade with a peer and solve his/her puzzle.