# Thread: Math models and equations

1. ## Math models and equations

Bascially if you pick any number and then Multiply it by two. Add seven. Multiply by three. Add the number you first thought of. Divide by seven. Multiply by four. Subtract the number you first thought of. Divide by three. Subtract the number you first thought of again.

The answer will always be 4.

If you take x to be the first number you though of, and y to be the result.
How would you write and equation expressing y as a function of the operations on x described above.

Also how would you simplify this equation, which would explain the final result?

Any help on this would be appreciated.

2. Originally Posted by newatthis

Bascially if you pick any number and then Multiply it by two. Add seven. Multiply by three. Add the number you first thought of. Divide by seven. Multiply by four. Subtract the number you first thought of. Divide by three. Subtract the number you first thought of again.

The answer will always be 4.

If you take x to be the first number you though of, and y to be the result.
How would you write and equation expressing y as a function of the operations on x described above.

Also how would you simplify this equation, which would explain the final result?

Any help on this would be appreciated.
Do what it says!
If you start with x and "Multiply it by 2" you have 2x. "Add 7": 2x+ 7. "Multiply by 3": 3(2x+ 7)= 6x+ 21. "Add the number you first thought of",which is x: (6x+ 21)+ x= 7x+ 21.

Can you finish? This is really an exercise in your ability to follow directions!

3. Originally Posted by newatthis

Bascially if you pick any number and then Multiply it by two. Add seven. Multiply by three. Add the number you first thought of. Divide by seven. Multiply by four. Subtract the number you first thought of. Divide by three. Subtract the number you first thought of again.

The answer will always be 4.

If you take x to be the first number you thought of, and y to be the result.
How would you write an equation expressing y as a function of the operations on x described above.

Also how would you simplify this equation, which would explain the final result?

Any help on this would be appreciated.
Hello newatthis,

This is the way it would look before simplifying using a minimum number of grouping symbols. Test it with a number of your choice to be sure. Then, attempt to simplify it.

$\displaystyle y=\frac{\frac{(x \cdot 2+7) \cdot 3+x}{7} \cdot 4 -x}{3}-x$

4. ## Thanks! and another Q

Thanks to both of you for replying. I understand it much better now and have managed to simplify it

Could someone help me understand why the answer is always 4?