SOLUTION: I have a word problem my son and I can't figure out. I would appreciate any help you can give. 10 triangles weigh as much as 3 squares and 1 circle. 2 triangles and 1 circle are

Question 558532: I have a word problem my son and I can't figure out. I would appreciate any help you can give.
10 triangles weigh as much as 3 squares and 1 circle. 2 triangles and 1 circle are equal in weight to 1 square. How many triangles weigh as much as 1 square.
thank you for your help.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
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:
= weight of 1 triangle
= weight of 1 circle
= weight of 1 square
"10 triangles weigh as much as 3 squares and 1 circle" can be written as

"2 triangles and 1 circle are equal in weight to 1 square" can be written as

We have two equations with 3 variables:
=

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 and as a function of :

We can simplify, eliminating and collecting like terms to get

Dividing by 4 both sides we get
which is the answer to the problem.
Three triangles weigh as much as 1 square.

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