People Don't Have 6 Arms

Algebra Level 2

In your living room, there is one coffee table and six times as many arms as people. If there are 34 legs in the room, how many people are there?

Details and Assumptions:

The coffee table has 4 legs.
Armchairs have 2 arms and 4 legs.
People have 2 arms and 2 legs.

5 4 6 3

2 solutions

Zandra Vinegar Staff
Feb 18, 2016

Let $P$ be the number of people in the room and $C$ be the number of chairs.
Additionally, let $L$ be the number of legs in the room and $A$ the number of arms.
We are given that $L = 34,$ and that $A = 6P.$

Additionally, because the table has four legs, each char has four legs, and each person has two legs:
$L = 4 + 4C + 2P$ and, similarly for arms: $A = 2C + 2P.$

Combining all four equations, we have that:

$6P = 2C + 2P$
$\rightarrow 4P = 2C$ $\rightarrow 2P = C$

$34 = 4 + 4C + 2P$
$\rightarrow 30 = 4C + 2P$
$\rightarrow 30 = 4C + C = 5C$
$\rightarrow 6 = C = 2P$
$\rightarrow \fbox{3 = P}$

Therefore, there are three people in the room (in addition to 6 armchairs and 1 table).

I reasoned one armchair for every person in the room, thereby getting 5 as the answer.

Pulkit Gupta - 5 years, 3 months ago

One armchair per person would give you 4 arms per person: two human arms and two chair arms. You need two armchairs per person in order to have 6 arms in the room per person.

Zandra Vinegar Staff - 5 years, 3 months ago

Yeah, I feel silly on having missed that line of reasoning :-)

Pulkit Gupta - 5 years, 3 months ago

Moses Loh
Feb 20, 2016

Basically: [34 - 4 -(6x4)]/2

People Don't Have 6 Arms

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