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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

$4$ $4$ tables and $9$ $9$ chairs

Explanation:

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

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

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

Therefore
$XXX 2 t + 1 = 3 (t - 1)$ $color(white)("XXX")2t+1=3(t-1)$

$XXX 2 t + 1 = 3 t - 3$ $color(white)("XXX")2t+1=3t-3$

$XXX 4 = t$ $color(white)("XXX")4=t$

and since $c = 2 t + 1$ $c=2t+1$
$XXX c = 2 \times 4 + 1 = 9$ $color(white)("XXX")c=2xx4+1=9$

Nov 15, 2016

4 tables 9 chairs

Explanation:

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

Breaking down the question into its component parts:

$If I have two chairs at each table I have an extra chair$ $color(brown)("If I have two chairs at each table I have an extra chair")$

$c = 2 t + 1$ $c=2t+1$

$If I have one table to three chairs I have 1 table with no chairs$ $color(brown)("If I have one table to three chairs I have 1 table with no chairs")$

$c = 3 (t - 1)$ $c=3(t-1)$

$\Rightarrow 2 t + 1 = c = 3 (t - 1)$ $=>2t+1=c=3(t-1)$

$2 t + 1 = 3 t - 3$ $2t+1=3t-3$

$3 t - 2 t = 1 + 3$ $3t-2t=1+3$

$t = 4$ $t=4$

But $c = 2 t + 1$ $c=2t+1$

$\Rightarrow c = 2 (4) + 1 = 9$ $=>c=2(4)+1=9$

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