Question

A room contains 55 chairs arranged in rows. The number of rows is one more than twice the number of chairs per row. Find the number of rows.

Answer 1

Answer:

i believe its 27

Step-by-step explanation:25 times two= 50 27 times two= 54 +one more is 55. so it is 27

Answer 2

Answer:

11 rows.

Step-by-step explanation:

Givens

• The room contains 55 chairs arranged in rows.
• The number of rows is one more than twice the number of chairs.

We know that the total number of chairs must be the product between the number of chairs per row and the total number of rows, which can be expressed as

$c \times r = 55$

Where $c$ represents the number of chairs per row and $r$ representes the number of rows.

The second given statment defined a second equation

$r=2c+1$

Now, we can substitute the second equation into the first one, and solve

$c \times r = 55\\c (2c+1)=55\\2c^{2}+c-55=0$

Which can be factored by multiplying the expression by 2, and solve has a perfect trinomial

$2(2c^{2}+c-55)=0\\2^{2}c^{2}+2c- 110=0\\(2c)^{2}+2c-110=0$

So, we need to find two number which product is 110 and is 1. If you think this through, those numbers are 11 and 10, because 11*10=110 and 11-10=1.

The factors are

$\frac{(2c+11)(2c-10)}{2} =0$, we have to divide by the number we multiplied before, then we simplify this number with the second factor

$(2c+11)(c-5)=0$

Where the positive solution is the only one that can be part of the answer because it doesn't make sense if we say -3 chairs. So,

$c-5=0\\c=5$

This means there are 5 chairs per row.

Then, we use this value to find the other one.

$c \times r=55\\5 \times r=55\\r=\frac{55}{5}\\ r=11$

Therefore, there are 11 rows and 5 chairs per row.