document.write( "Question 558532: I have a word problem my son and I can't figure out. I would appreciate any help you can give.
\n" ); document.write( "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.
\n" ); document.write( "thank you for your help.
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Algebra.Com's Answer #363082 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hopefully your son is familiar with algebra and with systems of equations.
\n" ); document.write( "We have to start by defining some variables, and I like to use letters that remind me of the meaning of the variable:
\n" ); document.write( " $\"t\"$ = weight of 1 triangle
\n" ); document.write( " $\"c\"$ = weight of 1 circle
\n" ); document.write( " $\"s\"$ = weight of 1 square
\n" ); document.write( "\"10 triangles weigh as much as 3 squares and 1 circle\" can be written as
\n" ); document.write( " $\"10t=3s%2Bc\"$
\n" ); document.write( "\"2 triangles and 1 circle are equal in weight to 1 square\" can be written as
\n" ); document.write( " $\"2t%2Bc=s\"$
\n" ); document.write( "We have two equations with 3 variables:
\n" ); document.write( " $\"10t\"$ = $\"3s%2Bc\"$
\n" ); document.write( " $\"2t%2Bc=s\"$
\n" ); document.write( "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 $\"s\"$ :
\n" ); document.write( " $\"10t%2B2t%2Bc=3s%2Bc%2Bs\"$
\n" ); document.write( "We can simplify, eliminating $\"c\"$ and collecting like terms to get
\n" ); document.write( " $\"12t=4s\"$
\n" ); document.write( "Dividing by 4 both sides we get
\n" ); document.write( " $\"3t=s\"$ which is the answer to the problem.
\n" ); document.write( "Three triangles weigh as much as 1 square.\r
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