# The hall had 160 seats. After the reconstruction every row had one seat added to them, and the number of rows doubled. How many seats were before and after the reconstruction, if the number of seats increased by 38?

##### 2 Answers

Solution 2 of 2

Assumption the declared count of seats is the initial count before the change.

#### Explanation:

The beginning of the question clearly states a count of seats as being 160. What is not clear is if this is the initial count or the count after the change. If you assume it is the initial count the numbers go wrong.

Let initial count of seats per row be

Let the initial count of rows be

Assumed that the initial total count of seats be 160

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Every row has 1 seat added

The count of rows is doubled

The count of seats increases by 38

Giving:

Divide both sides by 2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using

Subtract 160 from both sides

Solution 1 of 2

#### Explanation:

Let initial count of seats per row be

Let the initial count of rows be

Let the initial total count of seats be

Assumed that the final total count of seats is 160

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Every row has 1 seat added

The count of rows is doubled

The count of seats increases by 38

Thus

Divide both sides by 2

Substitute for

You will not have parts of a seat