Arthur has completed four times as many jigsaw puzzles as Conan. Doyle has completed three times as many jigsaw puzzles as Conan. Doyle has completed 12 fewer jigsaw puzzles than Arthur has. How many jigsaw puzzles has Conan completed?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Let us say puzzles solved by :

Arthur be x

Conan be y

Doyle be z

also,

Here, it is given that :

Arthur has completed four times as many jigsaw puzzles as Conan which means :

x = 4y.......(1)

Doyle has completed three times as many jigsaw puzzles as Conan which means :

z = 3y.....(2)

Doyle has completed 12 fewer jigsaw puzzles than Arthur has means :

z = x-12....(3)

now, to find the number of jigsaw puzzles does Conan (y) we equate equation (2) and (3) to find the value of y also by putting value of x in equation (3) :

3y = x-12

3y = 4y-12

4y-3y = 12

y = 12

Therefore, Canon has 12 jigsaw puzzles in total.