eroshea
a piece of cardboard has an area of 486 cm^2. a square of side 3cm is cut from each corner and an open box is made by turning up the ends and sides if the volume of the box formed is 756cm^3. what are the dimensions of the cardboard?
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hartnn
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drawing a figure will help, could u draw a figure of this ?
eroshea
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|dw:1353637103770:dw|
hartnn
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|dw:1353579949506:dw|
hartnn
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volume = 3(x-6)(y-6) = 756
hartnn
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can u solve those 2 equations ?
xy=486
3(x-6)(y-6) = 756
?
eroshea
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cAN I DO the substitution method?
eroshea
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x = 486/y
then substitute to the second equation
hartnn
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try it, if u go wrong, i'll help....
instead substitute xy=486 in 2nd equation
hartnn
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u get xy term in 2nd equation
hartnn
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and u'll be able to find x+y from 2nd equation...
eroshea
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18y^2-810y+8748
very big numbers >.<
hartnn
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y^2-45y+486
hartnn
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if 18y^2-810y+8748 is correct... i have not checked that.
hartnn
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y^2-45y+486 =0 is correct
can u factor it ?
hartnn
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hint : 18*27 = 486
hartnn
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y^2-45y+486 =0
(y-18)(y-27)=0
hartnn
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find y from here, then u also get 2 values of x
then dimensions are x,y
eroshea
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you're a very big help to me my friend. thanks a lot :)