Given a number of 3 i n squares and 2 i n squares, how many of each are needed to ge

kramberol

kramberol

Answered question

2022-07-01

Given a number of 3 i n squares and 2 i n squares, how many of each are needed to get a total area of 35 i n 2 ?
Through quick trial and error (the method they wanted I believe) you find that you need 3 3 i n squares and 2 2 i n squares, but I got to thinking on how to solve this exactly.
You have 2 unknowns and the following info:
4 x + 9 y = 35
x 0 ,   y 0 ,   x   and   y are both integers.
It also follows then that x 8   and   y 3

Answer & Explanation

Tanner Hamilton

Tanner Hamilton

Beginner2022-07-02Added 12 answers

A quick way to see the answer is to convert both sides of the equation mod 4. So the left hand side is y (mod 4) (because 4 = 0 , 9 = 1 mod 4), and the right hand side is 3 (mod 4). So y = 3 mod 4. Since y 3 as you observed, the only solution (if there is any ) is y = 3. Then you check that 4 x + 27 = 35 and hence x = 2.

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