Question 558532
Hopefully your son is familiar with algebra and with systems of equations.
We have to start by defining some variables, and I like to use letters that remind me of the meaning of the variable:
{{{t}}} =  weight of 1 triangle
{{{c}}} = weight of 1 circle
{{{s}}} = weight of 1 square
"10 triangles weigh as much as 3 squares and 1 circle" can be written as
{{{10t=3s+c}}}
"2 triangles and 1 circle are equal in weight to 1 square" can be written as
{{{2t+c=s}}}
We have two equations with 3 variables:
{{{10t}}} = {{{3s+c}}}
{{{2t+c=s}}}
Let's add both equations, to get the sum of the left hand sides equal to the sum of the right hand sides, to try to find the values of {{{t}}} and {{{c}}} as a function of {{{s}}}:
{{{10t+2t+c=3s+c+s}}}
We can simplify, eliminating {{{c}}} and collecting like terms to get
{{{12t=4s}}}
Dividing by 4 both sides we get
{{{3t=s}}} which is the answer to the problem.
Three triangles weigh as much as 1 square.