Algebra

posted by on .

Here's another problem I'm having a little trouble with:

A piece of string is 40 cm long. It is cut into three pieces. The longest piece is 3 times as long as the middle-sized piece, and the shortest piece is 23 cm shorter than the longest piece. Find the lengths of the three pieces.

What could be an equation I could write?

Thank you so much!

• Algebra - ,

call the middle size m
then the long piece is 3 m
and the short piece is 3m-23
so
(3m-23) + m + 3m = 40
7 m -23 = 40
solve for m

• Algebra - ,

Thank you very much!

• Algebra - ,

7m - 23 =40
+ 23 +23
then 7m=63
then you divide 63 by 7 it equal 9
so the ans. is m=9 :)

• Algebra - ,

let the shortest piece be x cm

<the shortest piece is 23 cm shorter than the longest piece> or
the longest piece is 23 more than the shortest piece,
so longest = x+23

<The longest piece is 3 times as long as the middle-sized piece> or
the middle piece is 1/3 of the longest piece,
so middle piece = 1/3(x+23)

then x + (x+23) + 1/3(x+23) = 40

(I get x=4, for the shortest piece of 4 cm)

• Algebra - ,

Thanks!

• Algebra - ,