# I have some chair and tables.If i place two chair at each table ,I have extra chair.If i place 3 chairs at each table,i have one table with no chairs.What is the sum of the total umber of tables and chairs?

## IQ question ,please ans anyhow and fast

##### 2 Answers
Nov 15, 2016

$4$ tables and $9$ chairs

#### Explanation:

Let $t$ be the number of tables
and $c$ be the number of chairs.

If I place two chairs at each table, I have extra chair.
$\rightarrow c = 2 t + 1$

If I place 3 chairs at each table, I have one table with no chairs.
$\rightarrow c = 3 \left(t - 1\right)$

Therefore
$\textcolor{w h i t e}{\text{XXX}} 2 t + 1 = 3 \left(t - 1\right)$

$\textcolor{w h i t e}{\text{XXX}} 2 t + 1 = 3 t - 3$

$\textcolor{w h i t e}{\text{XXX}} 4 = t$

and since $c = 2 t + 1$
$\textcolor{w h i t e}{\text{XXX}} c = 2 \times 4 + 1 = 9$

Nov 15, 2016

4 tables 9 chairs

#### Explanation:

Let the count of chairs be $c$
Let the count of tables be $t$

Breaking down the question into its component parts:

$\textcolor{b r o w n}{\text{If I have two chairs at each table I have an extra chair}}$

$c = 2 t + 1$

$\textcolor{b r o w n}{\text{If I have one table to three chairs I have 1 table with no chairs}}$

$c = 3 \left(t - 1\right)$

$\implies 2 t + 1 = c = 3 \left(t - 1\right)$

$2 t + 1 = 3 t - 3$

$3 t - 2 t = 1 + 3$

$t = 4$

But $c = 2 t + 1$

$\implies c = 2 \left(4\right) + 1 = 9$