maths question solution please

[idl]

circle + triangle = square
square + square = hexagon
circle + circle+ triangle = hexagon
what is the value of triangle? if all the shapes are numbers

[Guest55]

circle + triangle = square
square + square = hexagon
circle + circle+ triangle = hexagon
what is the value of triangle? if all the shapes are numbers

Replace square in second statement by circle + triangle.

circle + triangle + circle + triangle = hexagon

Then compare to third statement. Can you see the answer now?

[anotherdad]

It's the same problem as Bananaperson's thread entitled 'Help'. My solution is below but Guest55's is better because it's more straightforward.

Since circle+triangle=square, you can substitute a square in place of (circle+triangle) in line 3 to give circle+square=hexagon.

From line 2, you can then deduce that circle=square because we now have circle+square=hexagon in line 3 as well as square+square=hexagon in line 2. In other words, adding a circle to a square has the same effect (resulting in a hexagon) as adding a square to a square.

From line 1, now we know that circle=square, that must mean that triangle=0 because adding triangle to a circle doesn't change its value.

(which means that circle=1, square=1 and hexagon=2)

[idl]

hi ..
Thanks a lot both of you.
I worked out the ans as triangle =0 from many approaches but couldn't convince myself if circle and square have the same value.
Ofcourse the question doesn't say they are given different numbers so...it should be correct.

Thanks again.

[Guest55]

(which means that circle=1, square=1 and hexagon=2)

I think there will be a whole family of solutions? circle = square = n and hexagon = 2n

[Surferfish]

Yes I agree.

Triangle has to equal zero but circle and square can equal any number. (and hexagon can equal any number times 2)