A Leg to Stand On
Can you work out the number of chairs at a cafe from the number of legs?
Age
11 to 14
Challenge level
Problem
In the Soft Boulder Cafe, each table has 3 legs, each chair has 4 legs and all the customers and the three members of staff have two legs each. There are four chairs at each table.
At a certain time, three-quarters of the chairs are occupied by customers and there are 206 legs altogether in the cafe.
How many chairs does the cafe have?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Getting Started
Student Solutions
Answer: 32
Count the legs around each table:
Image
So there are 3 + 16 + 6 = 25 legs for each table.
206 legs - the 6 legs of the staff = 200 legs
200 legs = 8 tables
8 tables require 32 chairs.